answers (lesson 7-1) · pdf fileanswers name ... lesson 7-1 f ind the geometric mean between...
TRANSCRIPT
© Glencoe/McGraw-Hill A3 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Geo
met
ric
Mea
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
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__P
ER
IOD
____
_
7-1
7-1
©G
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w-H
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3G
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eom
etry
Lesson 7-1
Fin
d t
he
geom
etri
c m
ean
bet
wee
n e
ach
pai
r of
nu
mb
ers.
Sta
te e
xact
an
swer
s an
dan
swer
s to
th
e n
eare
st t
enth
.
1.2
and
82.
9 an
d 36
3.4
and
7
418
�28�
�5.
3
4.5
and
105.
2�2�
and
5�2�
6.3�
5�an
d 5�
5�
�50�
�7.
1�
20��
4.5
�75�
�8.
7
Fin
d t
he
mea
sure
of
each
alt
itu
de.
Sta
te e
xact
an
swer
s an
d a
nsw
ers
to t
he
nea
rest
ten
th.
7.8.
�14�
�3.
7�
24��
4.9
9.10
.
�18�
�4.
26
Fin
d x
and
y.
11.
12.
6;�
108
��
10.4
�40�
�6.
3;�
56��
7.5
13.
14.
�60�
�7.
7;�
285
��
16.9
12.5
;�
29��
5.425y
x
15
4
y
x
10
4
yx
39y
x
RT
S U4.
58
GEH
F
2
9
L
M N
P2
12
C
D
B
A2
7
©G
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w-H
ill35
4G
lenc
oe G
eom
etry
Fin
d t
he
geom
etri
c m
ean
bet
wee
n e
ach
pai
r of
nu
mb
ers
to t
he
nea
rest
ten
th.
1.8
and
122.
3�7�
and
6�7�
3.�4 5�
and
2
�96�
�9.
8�
126
��
11.2
���8 5��
1.3
Fin
d t
he
mea
sure
of
each
alt
itu
de.
Sta
te e
xact
an
swer
s an
d a
nsw
ers
to t
he
nea
rest
ten
th.
4.5.
�60�
�7.
7�
102
��
10.1
Fin
d x
,y,a
nd
z.
6.7.
�18
4�
�13
.6;
�24
8�
�15
.7;
�11
4�
�10
.7;
�15
0�
�12
.2;
�71
3�
�26
.7�
475
��
21.8
8.9.
4.5;
�13�
�3.
6;6.
515
;5;
�30
0�
�17
.3
10.C
IVIL
EN
GIN
EER
ING
An
airp
ort,
a fa
ctor
y,an
d a
shop
ping
cen
ter
are
at t
he v
erti
ces
of a
righ
t tr
iang
le f
orm
ed b
y th
ree
high
way
s.T
he a
irpo
rt a
nd f
acto
ry a
re 6
.0 m
iles
apa
rt.T
heir
dist
ance
s fr
om t
he s
hopp
ing
cent
er a
re 3
.6 m
iles
and
4.8
mil
es,r
espe
ctiv
ely.
A s
ervi
ce r
oad
wil
l be
con
stru
cted
fro
m t
he s
hopp
ing
cent
er t
o th
e hi
ghw
ay t
hat
conn
ects
the
air
port
and
fact
ory.
Wh
at i
s th
e sh
orte
st p
ossi
ble
len
gth
for
th
e se
rvic
e ro
ad?
Rou
nd
to t
he
nea
rest
hu
ndr
edth
.2.
88 m
i
xy10
z
20x
y 2
3
z
zx
y625
23
z
xy
8
17
6
KLJ
M
125
U
TA
V
Pra
ctic
e (
Ave
rag
e)
Geo
met
ric
Mea
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
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__P
ER
IOD
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_
7-1
7-1
Answers (Lesson 7-1)
© Glencoe/McGraw-Hill 354 Glencoe Geometry
Find the geometric mean between each pair of numbers to the nearest tenth.
1. 8 and 12 2. 3�7� and 6�7� 3. �45� and 2
Find the measure of each altitude. State exact answers and answers to the nearesttenth.
4. 5.
Find x, y, and z.
6. 7.
8. 9.
10. CIVIL ENGINEERING An airport, a factory, and a shopping center are at the vertices of aright triangle formed by three highways. The airport and factory are 6.0 miles apart. Theirdistances from the shopping center are 3.6 miles and 4.8 miles, respectively. A service roadwill be constructed from the shopping center to the highway that connects the airport andfactory. What is the shortest possible length for the service road? Round to the nearesthundredth.
x y
10z
20x
y
2
3
z
zx y
625
23
z
xy
8
17
6
KL
J M
125
U
T A V
Practice Geometric Mean
NAME ______________________________________________ DATE ____________ PERIOD _____
7-17-1
© Glencoe/McGraw-Hill A6 Glencoe Geometry
Skil
ls P
ract
ice
Th
e P
yth
ago
rean
Th
eore
m a
nd
Its
Co
nver
se
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
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__P
ER
IOD
____
_
7-2
7-2
©G
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etry
Lesson 7-2
Fin
d x
.
1.2.
3.
155
�11
68�
�34
.2
4.5.
6.
�46
8.7
�5�
�21
.7�
65��
8.1
�11
57�
�34
.0
Det
erm
ine
wh
eth
er �
ST
Uis
a r
igh
t tr
ian
gle
for
the
give
n v
erti
ces.
Exp
lain
.
7.S
(5,5
),T
(7,3
),U
(3,2
)8.
S(3
,3),
T(5
,5),
U(6
,0)
no
;S
T�
�8�,
TU
��
17�,
yes;
ST
��
8�,T
U�
�26�
,
US
��
13�,
US
��
18�,
( �8�)
2�
( �13�
)2�
( �17�
)2( �
8�)2
� ( �
18�)2
�( �
26�)2
9.S
(4,6
),T
(9,1
),U
(1,3
)10
.S(0
,3),
T(�
2,5)
,U(4
,7)
yes;
ST
��
50�,T
U�
�68�
,ye
s;S
T�
�8�,
TU
��
40�,
US
��
18�,
US
��
32�,
( �18�
)2�
( �50�
)2�
( �68�
)2( �
8�)2
� ( �
32�)2
�( �
40�)2
11.S
(�3,
2),T
(2,7
),U
(�1,
1)12
.S(2
,�1)
,T(5
,4),
U(6
,�3)
yes;
ST
��
50�,T
U�
�45�
,n
o;
ST
��
34�,T
U�
�50�
,
US
��
5�,U
S�
�20�
,( �
45�)2
� ( �
5�)2
�( �
50�)2
( �34�
)2�
( �20�
)2�
( �50�
)2
Det
erm
ine
wh
eth
er e
ach
set
of
mea
sure
s ca
n b
e th
e m
easu
res
of t
he
sid
es o
f a
righ
t tr
ian
gle.
Th
en s
tate
wh
eth
er t
hey
for
m a
Pyt
hag
orea
n t
rip
le.
13.1
2,16
,20
14.1
6,30
,32
15.1
4,48
,50
yes,
yes
no
,no
yes,
yes
16.�
2 5� ,�4 5� ,
�6 5�17
.2�
6�,5,
718
.2�
2�,2�
7�,6
no
,no
yes,
no
yes,
nox31
14x
99
8
x12
.5
25
x
1232
x
12
13x 12
9
©G
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0G
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eom
etry
Fin
d x
.
1.2.
3.
�69
8�
�26
.4�
715
��
26.7
�59
5�
�24
.4
4.5.
6.
�16
40�
�40
.5�
60��
7.7
�13
5�
�11
.6
Det
erm
ine
wh
eth
er �
GH
Iis
a r
igh
t tr
ian
gle
for
the
give
n v
erti
ces.
Exp
lain
.
7.G
(2,7
),H
(3,6
),I(
�4,
�1)
8.G
(�6,
2),H
(1,1
2),I
(�2,
1)
yes;
GH
��
2�,H
I��
98�,
no
;G
H�
�14
9�
,HI�
�13
0�
,
IG�
�10
0�
,IG
��
17�,
( �2�)
2�
( �98�
)2�
( �10
0�
)2( �
130
�)2
� ( �
17�)2
�( �
149
�)2
9.G
(�2,
1),H
(3,�
1),I
(�4,
�4)
10.G
(�2,
4),H
(4,1
),I(
�1,
�9)
yes;
GH
��
29�,H
I��
58�,
yes;
GH
��
45�,H
I� �
125
�,
IG�
�29�
,IG
��
170
�,
( �29�
)2�
( �29�
)2�
( �58�
)2( �
45�)2
� ( �
125
�)2
�( �
170
�)2
Det
erm
ine
wh
eth
er e
ach
set
of
mea
sure
s ca
n b
e th
e m
easu
res
of t
he
sid
es o
f a
righ
t tr
ian
gle.
Th
en s
tate
wh
eth
er t
hey
for
m a
Pyt
hag
orea
n t
rip
le.
11.9
,40,
4112
.7,2
8,29
13.2
4,32
,40
yes,
yes
no
,no
yes,
yes
14.�
9 5� ,�1 52 �
,315
.�1 3� ,
,116
.,
,�4 7�
yes,
no
yes,
no
yes,
no
17.C
ON
STR
UC
TIO
NT
he
bott
om e
nd
of a
ram
p at
a w
areh
ouse
is
10 f
eet
from
th
e ba
se o
f th
e m
ain
doc
k an
d is
11
feet
lon
g.H
ow
hig
h i
s th
e do
ck?
abo
ut
4.6
ft h
igh
11 ft
?dock
ram
p
10 ft
2�3�
�7
�4�
�7
2 �2�
�3
x24
24
42
x16
14
x
34
22
x26
2618
x
3421
x
13
23Pra
ctic
e (
Ave
rag
e)
Th
e P
yth
ago
rean
Th
eore
m a
nd
Its
Co
nver
se
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-2
7-2
Answers (Lesson 7-2)
© Glencoe/McGraw-Hill 360 Glencoe Geometry
Find x.
1. 2. 3.
4. 5. 6.
Determine whether �GHI is a right triangle for the given vertices. Explain.
7. G(2, 7), H(3, 6), I(�4, �1) 8. G(�6, 2), H(1, 12), I(�2, 1)
9. G(�2, 1), H(3, �1), I(�4, �4) 10. G(�2, 4), H(4, 1), I(�1, �9)
Determine whether each set of measures can be the measures of the sides of aright triangle. Then state whether they form a Pythagorean triple.
11. 9, 40, 41 12. 7, 28, 29 13. 24, 32, 40
14. �95�, �
152�, 3 15. �
13�, , 1 16. , , �
47�
17. CONSTRUCTION The bottom end of a ramp at a warehouse is 10 feet from the base of the main dock and is 11 feet long. How high is the dock?
11 ft?
dock
ramp
10 ft
2�3��7
�4��7
2�2��3
x2424
42
x16
14
x
34
22
x26
2618
x
34 21x
13
23
Practice The Pythagorean Theorem and Its Converse
NAME ______________________________________________ DATE ____________ PERIOD _____
7-27-2
© Glencoe/McGraw-Hill A9 Glencoe Geometry
An
swer
s
Skil
ls P
ract
ice
Sp
ecia
l Rig
ht T
rian
gle
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-3
7-3
©G
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cGra
w-H
ill36
5G
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eom
etry
Lesson 7-3
Fin
d x
and
y.
1.2.
3.
12,1
2�3�
64,3
2�3�
6�2�,
6�2�
4.5.
6.
8,8�
2�8,
8�3�
45,1
3�2�
For
Exe
rcis
es 7
–9,u
se t
he
figu
re a
t th
e ri
ght.
7.If
a�
11,f
ind
ban
d c.
b�
11�
3�;c
�22
8.If
b�
15,f
ind
aan
d c.
a�
5�3�;
c�
10�
3�
9.If
c�
9,fi
nd
aan
d b.
a�
4.5;
b�
4.5�
3�
For
Exe
rcis
es 1
0 an
d 1
1,u
se t
he
figu
re a
t th
e ri
ght.
10.T
he
peri
met
er o
f th
e sq
uar
e is
30
inch
es.F
ind
the
len
gth
of
B�C�
.
7.5
in.
11.F
ind
the
len
gth
of
the
diag
onal
B�D�
.
7.5�
2�in
.or
abo
ut
10.6
1 in
.
12.T
he
peri
met
er o
f th
e eq
uil
ater
al t
rian
gle
is 6
0 m
eter
s.F
ind
the
le
ngt
h o
f an
alt
itu
de.
10�
3�m
or
abo
ut
17.3
2 m
13.�
GE
Cis
a 3
0°-6
0°-9
0°tr
ian
gle
wit
h r
igh
t an
gle
at E
,an
d E�
C�is
th
e lo
nge
r le
g.F
ind
the
coor
din
ates
of
Gin
Qu
adra
nt
I fo
r E
(1,1
) an
d C
(4,1
).
( 1,1
��
3�)o
r ab
ou
t (1
,2.7
3)
E
FG
D60
�
AB C
D45
�
bA
B Cac
60�
30�
y x� 13
1313
13
y
x60�
16
y
x
45�
8
y
x
45�
12
y
x
30�
32
y
x60
�24
©G
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w-H
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6G
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etry
Fin
d x
and
y.
1.2.
3.
,25
�3�,
5013
,13�
3�
4.5.
6.
45,1
4�2�
3.5�
3�,7
;11
�2�
For
Exe
rcis
es 7
–9,u
se t
he
figu
re a
t th
e ri
ght.
7.If
a�
4�3�,
fin
d b
and
c.
b�
12,c
�8�
3�
8.If
x�
3�3�,
fin
d a
and
CD
.
a�
6�3�,
CD
�9
9.If
a�
4,fi
nd
CD
,b,a
nd
y.
CD
�2�
3�,b
�4�
3�,y
�6
10.T
he
peri
met
er o
f an
equ
ilat
eral
tri
angl
e is
39
cen
tim
eter
s.F
ind
the
len
gth
of
an a
ltit
ude
of t
he
tria
ngl
e.
6.5�
3�in
.or
abo
ut
11.2
6 in
.
11.�
MIP
is a
30°
-60°
-90°
tria
ngl
e w
ith
rig
ht
angl
e at
I,a
nd
I�P�th
e lo
nge
r le
g.F
ind
the
coor
din
ates
of
Min
Qu
adra
nt
I fo
r I(
3,3)
an
d P
(12,
3).
( 3,3
�3�
3�)o
r ab
ou
t (3
,8.1
9)
12.�
TJ
Kis
a 4
5°-4
5°-9
0°tr
ian
gle
wit
h r
igh
t an
gle
at J
.Fin
d th
e co
ordi
nat
es o
f T
inQ
uad
ran
t II
for
J(�
2,�
3) a
nd
K(3
,�3)
.
(�2,
2)
13.B
OTA
NIC
AL
GA
RD
ENS
On
e of
th
e di
spla
ys a
t a
bota
nic
al g
arde
n
is a
n h
erb
gard
en p
lan
ted
in t
he
shap
e of
a s
quar
e.T
he
squ
are
mea
sure
s 6
yard
s on
eac
h s
ide.
Vis
itor
s ca
n v
iew
th
e h
erbs
fro
m a
diag
onal
pat
hw
ay t
hro
ugh
th
e ga
rden
.How
lon
g is
th
e pa
thw
ay?
6�2�
yd o
r ab
ou
t 8.
48 y
d
6 yd
6 yd
6 yd
6 yd
bA
B C
D
a
x
y60
�
30�
c
11�
2��
2
x
45�
11
y60
�3.
5
xy
x�y
28
9�2�
�2
9�2�
�2
y
x
30�
26y
x
2560�
yx
45�
9Pra
ctic
e (
Ave
rag
e)
Sp
ecia
l Rig
ht T
rian
gle
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
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__P
ER
IOD
____
_
7-3
7-3
Answers (Lesson 7-3)
© Glencoe/McGraw-Hill 366 Glencoe Geometry
Find x and y.
1. 2. 3.
4. 5. 6.
For Exercises 7–9, use the figure at the right.
7. If a � 4�3�, find b and c.
8. If x � 3�3�, find a and CD.
9. If a � 4, find CD, b, and y.
10. The perimeter of an equilateral triangle is 39 centimeters. Find the length of an altitudeof the triangle.
11. �MIP is a 30°-60°-90° triangle with right angle at I, and I�P� the longer leg. Find thecoordinates of M in Quadrant I for I(3, 3) and P(12, 3).
12. �TJK is a 45°-45°-90° triangle with right angle at J. Find the coordinates of T inQuadrant II for J(�2, �3) and K(3, �3).
13. BOTANICAL GARDENS One of the displays at a botanical garden is an herb garden planted in the shape of a square. The square measures 6 yards on each side. Visitors can view the herbs from adiagonal pathway through the garden. How long is the pathway?
6 yd 6 yd
6 yd
6 yd
bA
B
C
D
a
x
y60�
30�
c
x
45�
11
y60�3.5
xy
x�
y 28
y
x
30�
26y
x
25
60�
yx
45�9
Practice Special Right Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-37-3
Skills PracticeSpecial Right Triangles
NAME ______________________________________________ DATE ____________ PERIOD _____
7-37-3
© Glencoe/McGraw-Hill 365 Glencoe Geometry
Less
on
7-3
Find x and y.
1. 2. 3.
4. 5. 6.
For Exercises 7–9, use the figure at the right.
7. If a � 11, find b and c.
8. If b � 15, find a and c.
9. If c � 9, find a and b.
For Exercises 10 and 11, use the figure at the right.
10. The perimeter of the square is 30 inches. Find the length of B�C�.
11. Find the length of the diagonal B�D�.
12. The perimeter of the equilateral triangle is 60 meters. Find the length of an altitude.
13. �GEC is a 30°-60°-90° triangle with right angle at E, and E�C� is the longer leg. Find the coordinates of G in Quadrant I for E(1, 1) and C(4, 1).
E
FGD 60�
A B
CD 45�
bA
B
C
ac
60�
30�
y
x�
13
1313
13
y
x60�
16
y
x
45� 8
y
x
45�
12
y
x
30�
32
y
x60� 24
© Glencoe/McGraw-Hill A12 Glencoe Geometry
Skil
ls P
ract
ice
Trig
on
om
etry
NA
ME
____
____
____
____
____
____
____
____
____
____
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__D
AT
E__
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__P
ER
IOD
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_
7-4
7-4
©G
lenc
oe/M
cGra
w-H
ill37
1G
lenc
oe G
eom
etry
Lesson 7-4
Use
�R
ST
to f
ind
sin
R,c
os R
,tan
R,s
in S
,cos
S,a
nd
tan
S.
Exp
ress
eac
h r
atio
as
a fr
acti
on a
nd
as
a d
ecim
al t
o th
e n
eare
st h
un
dre
dth
.
1.r
�16
,s�
30,t
�34
2.r
�10
,s�
24,t
�26
sin
R�
�1 36 4��
0.47
;si
n R
��1 20 6�
�0.
38;
cos
R�
�3 30 4��
0.88
;co
s R
��2 24 6�
�0.
92;
tan
R�
�1 36 0��
0.53
;ta
n R
��1 20 4�
�0.
42;
sin
S�
�3 30 4��
0.88
;si
n S
��2 24 6�
�0.
92;
cos
S�
�1 36 4��
0.47
;co
s S
��1 20 6�
�0.
38;
tan
S�
�3 10 6��
1.88
tan
S�
�2 14 0��
2.4
Use
a c
alcu
lato
r to
fin
d e
ach
val
ue.
Rou
nd
to
the
nea
rest
ten
-th
ousa
nd
th.
3.si
n 5
0.08
724.
tan
23
0.42
455.
cos
610.
4848
6.si
n 7
5.8
0.96
947.
tan
17.
30.
3115
8.co
s 52
.90.
6032
Use
th
e fi
gure
to
fin
d e
ach
tri
gon
omet
ric
rati
o.E
xpre
ss
answ
ers
as a
fra
ctio
n a
nd
as
a d
ecim
al r
oun
ded
to
the
nea
rest
ten
-th
ousa
nd
th.
9.ta
n C
10.s
in A
11.c
os C
� 49 0��
0.22
50�4 40 1�
�0.
9756
�4 40 1��
0.97
56
Fin
d t
he
mea
sure
of
each
acu
te a
ngl
e to
th
e n
eare
st t
enth
of
a d
egre
e.
12.s
in B
�0.
2985
17.4
13.t
an A
�0.
4168
22.6
14.c
os R
�0.
8443
32.4
15.t
an C
�0.
3894
21.3
16.c
os B
�0.
7329
42.9
17.s
in A
�0.
1176
6.8
Fin
d x
.Rou
nd
to
the
nea
rest
ten
th.
18.
19.
20.
28.8
73.5
15.9
19
x
33�
UL
S
27
x�8
BAC
27
x�
13 BA
C
41
409
B
A
C
sR
S Trt
©G
lenc
oe/M
cGra
w-H
ill37
2G
lenc
oe G
eom
etry
Use
�L
MN
to f
ind
sin
L,c
os L
,tan
L,s
in M
,cos
M,a
nd
tan
M.
Exp
ress
eac
h r
atio
as
a fr
acti
on a
nd
as
a d
ecim
al t
o th
e n
eare
st h
un
dre
dth
.
1.�
�15
,m�
36,n
�39
2.�
�12
,m�
12�
3�,n
�24
sin
L�
�1 35 9��
0.38
;si
n L
��1 22 4�
�0.
50;
cos
L�
�3 36 9��
0.92
;co
s L
��
0.87
;
tan
L�
�1 35 6��
0.42
;ta
n L
��
0.58
;
sin
M�
�3 36 9��
0.92
;si
n M
��
0.87
;
cos
M�
�1 35 9��
0.38
;co
s M
��1 22 4�
�0.
50;
tan
M�
�3 16 5��
2.4
tan
M�
�1.
73
Use
a c
alcu
lato
r to
fin
d e
ach
val
ue.
Rou
nd
to
the
nea
rest
ten
-th
ousa
nd
th.
3.si
n 9
2.4
0.99
914.
tan
27.
50.
5206
5.co
s 64
.80.
4258
Use
th
e fi
gure
to
fin
d e
ach
tri
gon
omet
ric
rati
o.E
xpre
ss
answ
ers
as a
fra
ctio
n a
nd
as
a d
ecim
al r
oun
ded
to
the
nea
rest
ten
-th
ousa
nd
th.
6.co
s A
7.ta
n B
8.si
n A
�0.
9487
�3 1��
3.00
00�
0.31
62
Fin
d t
he
mea
sure
of
each
acu
te a
ngl
e to
th
e n
eare
st t
enth
of
a d
egre
e.
9.si
n B
�0.
7823
51.5
10.t
an A
�0.
2356
13.3
11.c
os R
�0.
6401
50.2
Fin
d x
.Rou
nd
to
the
nea
rest
ten
th.
12.
64.4
13.
18.1
14.
24.2
15.G
EOG
RA
PHY
Die
go u
sed
a th
eodo
lite
to
map
a r
egio
n o
f la
nd
for
his
cl
ass
in g
eom
orph
olog
y.T
o de
term
ine
the
elev
atio
n o
f a
vert
ical
roc
kfo
rmat
ion
,he
mea
sure
d th
e di
stan
ce f
rom
th
e ba
se o
f th
e fo
rmat
ion
to
his
pos
itio
n a
nd
the
angl
e be
twee
n t
he
grou
nd
and
the
lin
e of
sig
ht
to
the
top
of t
he
form
atio
n.T
he
dist
ance
was
43
met
ers
and
the
angl
e w
as
36 d
egre
es.W
hat
is
the
hei
ght
of t
he
form
atio
n t
o th
e n
eare
st m
eter
?31
m
36� 43
m
41�
x
3229
x�9
23
x�
11
�10�
�10
3 �10�
�10
15
5��10
5 CA
B
12�
3��
12
12�
3��
2412� 12
�3�
12�
3��
24
ML
N
Pra
ctic
e (
Ave
rag
e)
Trig
on
om
etry
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
7-4
Answers (Lesson 7-4)
© Glencoe/McGraw-Hill A13 Glencoe Geometry
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csTr
igo
no
met
ry
NA
ME
____
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____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
7-4
©G
lenc
oe/M
cGra
w-H
ill37
3G
lenc
oe G
eom
etry
Lesson 7-4
Pre-
Act
ivit
yH
ow c
an s
urv
eyor
s d
eter
min
e an
gle
mea
sure
s?
Rea
d th
e in
trod
uct
ion
to
Les
son
7-4
at
the
top
of p
age
364
in y
our
text
book
.
•W
hy
is i
t im
port
ant
to d
eter
min
e th
e re
lati
ve p
osit
ion
s ac
cura
tely
in
nav
igat
ion
? (G
ive
two
poss
ible
rea
son
s.)
Sam
ple
an
swer
s:(1
) To
avo
id c
olli
sio
ns
bet
wee
n s
hip
s,an
d (
2) t
o p
reve
nt
ship
sfr
om
losi
ng
th
eir
bea
rin
gs
and
get
tin
g lo
st a
t se
a.•
Wh
at d
oes
cali
brat
edm
ean
? S
amp
le a
nsw
er:
mar
ked
pre
cise
ly t
op
erm
it a
ccu
rate
mea
sure
men
ts t
o b
e m
ade
Rea
din
g t
he
Less
on
1.R
efer
to
the
figu
re.W
rite
a r
atio
usi
ng
the
side
len
gth
s in
th
e
figu
re t
o re
pres
ent
each
of
the
foll
owin
g tr
igon
omet
ric
rati
os.
A.
sin
N� MM
NP �B
.cos
N� MN
P N�
C.
tan
N�M N
PP �D
.tan
M� MN
P P�
E.
sin
M� MN
P N�F.
cos
M� MM
NP �
2.A
ssu
me
that
you
en
ter
each
of
the
expr
essi
ons
in t
he
list
on
th
e le
ft i
nto
you
r ca
lcu
lato
r.M
atch
eac
h o
f th
ese
expr
essi
ons
wit
h a
des
crip
tion
fro
m t
he
list
on
th
e ri
ght
to t
ell
wh
atyo
u a
re f
indi
ng
wh
en y
ou e
nte
r th
is e
xpre
ssio
n.
P
MN
a.si
n 2
0v
b.
cos
20ii
c.si
n�
10.
8vi
d.
tan
�1
0.8
iiie.
tan
20
ivf.
cos�
10.
8i
i.th
e de
gree
mea
sure
of
an a
cute
an
gle
wh
ose
cosi
ne
is 0
.8
ii.
the
rati
o of
th
e le
ngt
h o
f th
e le
g ad
jace
nt
to t
he
20°
angl
e to
th
ele
ngt
h o
f h
ypot
enu
se i
n a
20°
-70°
-90°
tria
ngl
e
iii.
the
degr
ee m
easu
re o
f an
acu
te a
ngl
e in
a r
igh
t tr
ian
gle
for
wh
ich
th
e ra
tio
of t
he
len
gth
of
the
oppo
site
leg
to
the
len
gth
of
the
adja
cen
t le
g is
0.8
iv.t
he r
atio
of
the
leng
th o
f th
e le
g op
posi
te t
he 2
0°an
gle
to t
hele
ngth
of
the
leg
adja
cent
to
it i
n a
20°-
70°-
90°
tria
ngle
v.th
e ra
tio
of t
he
len
gth
of
the
leg
oppo
site
th
e 20
°an
gle
to t
he
len
gth
of
hyp
oten
use
in
a 2
0°-7
0°-9
0°tr
ian
gle
vi.t
he
degr
ee m
easu
re o
f an
acu
te a
ngl
e in
a r
igh
t tr
ian
gle
for
wh
ich
th
e ra
tio
of t
he
len
gth
of
the
oppo
site
leg
to
the
len
gth
of
the
hyp
oten
use
is
0.8
Hel
pin
g Y
ou
Rem
emb
er
3.H
ow c
an t
he
coin
cos
ine
hel
p yo
u t
o re
mem
ber
the
rela
tion
ship
bet
wee
n t
he
sin
es a
nd
cosi
nes
of
the
two
acu
te a
ngl
es o
f a
righ
t tr
ian
gle?
Sam
ple
an
swer
:Th
e co
in c
osi
ne
com
es f
rom
co
mp
lem
ent,
as in
com
ple
men
tary
ang
les.
Th
e co
sin
e o
f an
acu
te a
ng
le is
eq
ual
to
th
e si
ne
of
its
com
ple
men
t.
©G
lenc
oe/M
cGra
w-H
ill37
4G
lenc
oe G
eom
etry
Sin
e an
d C
osi
ne
of
An
gle
sT
he
foll
owin
g di
agra
m c
an b
e u
sed
to o
btai
n a
ppro
xim
ate
valu
es f
or t
he
sin
ean
d co
sin
e of
an
gles
fro
m 0
°to
90°
.Th
e ra
diu
s of
th
e ci
rcle
is
1.S
o,th
e si
ne
and
cosi
ne
valu
es c
an b
e re
ad d
irec
tly
from
th
e ve
rtic
al a
nd
hor
izon
tal
axes
.
Fin
d a
pp
roxi
mat
e va
lues
for
sin
40°
and
cos
40�
.Con
sid
er t
he
tria
ngl
e fo
rmed
by
the
segm
ent
mar
ked
40°
,as
illu
stra
ted
by
the
shad
ed
tria
ngl
e at
rig
ht.
sin
40°
��a c�
��0.
164 �or
0.6
4co
s 40
°�
�b c��
�0.177 �
or 0
.77
1.U
se t
he
diag
ram
abo
ve t
o co
mpl
ete
the
char
t of
val
ues
.
2.C
ompa
re t
he
sin
e an
d co
sin
e of
tw
o co
mpl
emen
tary
an
gles
(an
gles
wh
ose
sum
is
90°)
.Wh
at d
o yo
u n
otic
e?
Th
e si
ne
of
an a
ng
le is
eq
ual
to
th
e co
sin
e o
f th
e co
mp
lem
ent
of
the
ang
le.
00.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
90°
0°
10°
20°
30°
40°
50°
60°
70°
80°
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
7-4 x
°0°
10°
20°
30°
40°
50°
60°
70°
80°
90°
sin
x°
00.
170.
340.
50.
640.
770.
870.
940.
981
cos
x°
10.
980.
940.
870.
770.
640.
50.
340.
170
1 0
40°
0.64
c �
1 u
nit
x°b
� c
os x
°0.
771
a �
sin
x°
Exam
ple
Exam
ple
Answers (Lesson 7-4)
© Glencoe/McGraw-Hill 372 Glencoe Geometry
Use �LMN to find sin L, cos L, tan L, sin M, cos M, and tan M.Express each ratio as a fraction and as a decimal to the nearest hundredth.
1. � � 15, m � 36, n� 39 2. � � 12, m � 12�3�, n � 24
Use a calculator to find each value. Round to the nearest ten-thousandth.
3. sin 92.4 4. tan 27.5 5. cos 64.8
Use the figure to find each trigonometric ratio. Express answers as a fraction and as a decimal rounded to the nearest ten-thousandth.
6. cos A 7. tan B 8. sin A
Find the measure of each acute angle to the nearest tenth of a degree.
9. sin B � 0.7823 10. tan A � 0.2356 11. cos R � 0.6401
Find x. Round to the nearest tenth.
12. 13. 14.
15. GEOGRAPHY Diego used a theodolite to map a region of land for his class in geomorphology. To determine the elevation of a vertical rockformation, he measured the distance from the base of the formation to his position and the angle between the ground and the line of sight to the top of the formation. The distance was 43 meters and the angle was 36 degrees. What is the height of the formation to the nearest meter?
36�
43 m
41�x
3229
x �9
23
x �
11
15
5��105
CA
B
ML
N
Practice Trigonometry
NAME ______________________________________________ DATE ____________ PERIOD _____
7-47-4
© Glencoe/McGraw-Hill A12 Glencoe Geometry
Skil
ls P
ract
ice
Trig
on
om
etry
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
7-4
©G
lenc
oe/M
cGra
w-H
ill37
1G
lenc
oe G
eom
etry
Lesson 7-4
Use
�R
ST
to f
ind
sin
R,c
os R
,tan
R,s
in S
,cos
S,a
nd
tan
S.
Exp
ress
eac
h r
atio
as
a fr
acti
on a
nd
as
a d
ecim
al t
o th
e n
eare
st h
un
dre
dth
.
1.r
�16
,s�
30,t
�34
2.r
�10
,s�
24,t
�26
sin
R�
�1 36 4��
0.47
;si
n R
��1 20 6�
�0.
38;
cos
R�
�3 30 4��
0.88
;co
s R
��2 24 6�
�0.
92;
tan
R�
�1 36 0��
0.53
;ta
n R
��1 20 4�
�0.
42;
sin
S�
�3 30 4��
0.88
;si
n S
��2 24 6�
�0.
92;
cos
S�
�1 36 4��
0.47
;co
s S
��1 20 6�
�0.
38;
tan
S�
�3 10 6��
1.88
tan
S�
�2 14 0��
2.4
Use
a c
alcu
lato
r to
fin
d e
ach
val
ue.
Rou
nd
to
the
nea
rest
ten
-th
ousa
nd
th.
3.si
n 5
0.08
724.
tan
23
0.42
455.
cos
610.
4848
6.si
n 7
5.8
0.96
947.
tan
17.
30.
3115
8.co
s 52
.90.
6032
Use
th
e fi
gure
to
fin
d e
ach
tri
gon
omet
ric
rati
o.E
xpre
ss
answ
ers
as a
fra
ctio
n a
nd
as
a d
ecim
al r
oun
ded
to
the
nea
rest
ten
-th
ousa
nd
th.
9.ta
n C
10.s
in A
11.c
os C
� 49 0��
0.22
50�4 40 1�
�0.
9756
�4 40 1��
0.97
56
Fin
d t
he
mea
sure
of
each
acu
te a
ngl
e to
th
e n
eare
st t
enth
of
a d
egre
e.
12.s
in B
�0.
2985
17.4
13.t
an A
�0.
4168
22.6
14.c
os R
�0.
8443
32.4
15.t
an C
�0.
3894
21.3
16.c
os B
�0.
7329
42.9
17.s
in A
�0.
1176
6.8
Fin
d x
.Rou
nd
to
the
nea
rest
ten
th.
18.
19.
20.
28.8
73.5
15.9
19
x
33�
UL
S
27
x�8
BAC
27
x�
13 BA
C
41
409
B
A
C
sR
S Trt
©G
lenc
oe/M
cGra
w-H
ill37
2G
lenc
oe G
eom
etry
Use
�L
MN
to f
ind
sin
L,c
os L
,tan
L,s
in M
,cos
M,a
nd
tan
M.
Exp
ress
eac
h r
atio
as
a fr
acti
on a
nd
as
a d
ecim
al t
o th
e n
eare
st h
un
dre
dth
.
1.�
�15
,m�
36,n
�39
2.�
�12
,m�
12�
3�,n
�24
sin
L�
�1 35 9��
0.38
;si
n L
��1 22 4�
�0.
50;
cos
L�
�3 36 9��
0.92
;co
s L
��
0.87
;
tan
L�
�1 35 6��
0.42
;ta
n L
��
0.58
;
sin
M�
�3 36 9��
0.92
;si
n M
��
0.87
;
cos
M�
�1 35 9��
0.38
;co
s M
��1 22 4�
�0.
50;
tan
M�
�3 16 5��
2.4
tan
M�
�1.
73
Use
a c
alcu
lato
r to
fin
d e
ach
val
ue.
Rou
nd
to
the
nea
rest
ten
-th
ousa
nd
th.
3.si
n 9
2.4
0.99
914.
tan
27.
50.
5206
5.co
s 64
.80.
4258
Use
th
e fi
gure
to
fin
d e
ach
tri
gon
omet
ric
rati
o.E
xpre
ss
answ
ers
as a
fra
ctio
n a
nd
as
a d
ecim
al r
oun
ded
to
the
nea
rest
ten
-th
ousa
nd
th.
6.co
s A
7.ta
n B
8.si
n A
�0.
9487
�3 1��
3.00
00�
0.31
62
Fin
d t
he
mea
sure
of
each
acu
te a
ngl
e to
th
e n
eare
st t
enth
of
a d
egre
e.
9.si
n B
�0.
7823
51.5
10.t
an A
�0.
2356
13.3
11.c
os R
�0.
6401
50.2
Fin
d x
.Rou
nd
to
the
nea
rest
ten
th.
12.
64.4
13.
18.1
14.
24.2
15.G
EOG
RA
PHY
Die
go u
sed
a th
eodo
lite
to
map
a r
egio
n o
f la
nd
for
his
cl
ass
in g
eom
orph
olog
y.T
o de
term
ine
the
elev
atio
n o
f a
vert
ical
roc
kfo
rmat
ion
,he
mea
sure
d th
e di
stan
ce f
rom
th
e ba
se o
f th
e fo
rmat
ion
to
his
pos
itio
n a
nd
the
angl
e be
twee
n t
he
grou
nd
and
the
lin
e of
sig
ht
to
the
top
of t
he
form
atio
n.T
he
dist
ance
was
43
met
ers
and
the
angl
e w
as
36 d
egre
es.W
hat
is
the
hei
ght
of t
he
form
atio
n t
o th
e n
eare
st m
eter
?31
m
36� 43
m
41�
x
3229
x�9
23
x�
11
�10�
�10
3 �10�
�10
15
5��10
5 CA
B
12�
3��
12
12�
3��
2412� 12
�3�
12�
3��
24
ML
N
Pra
ctic
e (
Ave
rag
e)
Trig
on
om
etry
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
7-4
Answers (Lesson 7-4)
© Glencoe/McGraw-Hill A13 Glencoe Geometry
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csTr
igo
no
met
ry
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
7-4
©G
lenc
oe/M
cGra
w-H
ill37
3G
lenc
oe G
eom
etry
Lesson 7-4
Pre-
Act
ivit
yH
ow c
an s
urv
eyor
s d
eter
min
e an
gle
mea
sure
s?
Rea
d th
e in
trod
uct
ion
to
Les
son
7-4
at
the
top
of p
age
364
in y
our
text
book
.
•W
hy
is i
t im
port
ant
to d
eter
min
e th
e re
lati
ve p
osit
ion
s ac
cura
tely
in
nav
igat
ion
? (G
ive
two
poss
ible
rea
son
s.)
Sam
ple
an
swer
s:(1
) To
avo
id c
olli
sio
ns
bet
wee
n s
hip
s,an
d (
2) t
o p
reve
nt
ship
sfr
om
losi
ng
th
eir
bea
rin
gs
and
get
tin
g lo
st a
t se
a.•
Wh
at d
oes
cali
brat
edm
ean
? S
amp
le a
nsw
er:
mar
ked
pre
cise
ly t
op
erm
it a
ccu
rate
mea
sure
men
ts t
o b
e m
ade
Rea
din
g t
he
Less
on
1.R
efer
to
the
figu
re.W
rite
a r
atio
usi
ng
the
side
len
gth
s in
th
e
figu
re t
o re
pres
ent
each
of
the
foll
owin
g tr
igon
omet
ric
rati
os.
A.
sin
N� MM
NP �B
.cos
N� MN
P N�
C.
tan
N�M N
PP �D
.tan
M� MN
P P�
E.
sin
M� MN
P N�F.
cos
M� MM
NP �
2.A
ssu
me
that
you
en
ter
each
of
the
expr
essi
ons
in t
he
list
on
th
e le
ft i
nto
you
r ca
lcu
lato
r.M
atch
eac
h o
f th
ese
expr
essi
ons
wit
h a
des
crip
tion
fro
m t
he
list
on
th
e ri
ght
to t
ell
wh
atyo
u a
re f
indi
ng
wh
en y
ou e
nte
r th
is e
xpre
ssio
n.
P
MN
a.si
n 2
0v
b.
cos
20ii
c.si
n�
10.
8vi
d.
tan
�1
0.8
iiie.
tan
20
ivf.
cos�
10.
8i
i.th
e de
gree
mea
sure
of
an a
cute
an
gle
wh
ose
cosi
ne
is 0
.8
ii.
the
rati
o of
th
e le
ngt
h o
f th
e le
g ad
jace
nt
to t
he
20°
angl
e to
th
ele
ngt
h o
f h
ypot
enu
se i
n a
20°
-70°
-90°
tria
ngl
e
iii.
the
degr
ee m
easu
re o
f an
acu
te a
ngl
e in
a r
igh
t tr
ian
gle
for
wh
ich
th
e ra
tio
of t
he
len
gth
of
the
oppo
site
leg
to
the
len
gth
of
the
adja
cen
t le
g is
0.8
iv.t
he r
atio
of
the
leng
th o
f th
e le
g op
posi
te t
he 2
0°an
gle
to t
hele
ngth
of
the
leg
adja
cent
to
it i
n a
20°-
70°-
90°
tria
ngle
v.th
e ra
tio
of t
he
len
gth
of
the
leg
oppo
site
th
e 20
°an
gle
to t
he
len
gth
of
hyp
oten
use
in
a 2
0°-7
0°-9
0°tr
ian
gle
vi.t
he
degr
ee m
easu
re o
f an
acu
te a
ngl
e in
a r
igh
t tr
ian
gle
for
wh
ich
th
e ra
tio
of t
he
len
gth
of
the
oppo
site
leg
to
the
len
gth
of
the
hyp
oten
use
is
0.8
Hel
pin
g Y
ou
Rem
emb
er
3.H
ow c
an t
he
coin
cos
ine
hel
p yo
u t
o re
mem
ber
the
rela
tion
ship
bet
wee
n t
he
sin
es a
nd
cosi
nes
of
the
two
acu
te a
ngl
es o
f a
righ
t tr
ian
gle?
Sam
ple
an
swer
:Th
e co
in c
osi
ne
com
es f
rom
co
mp
lem
ent,
as in
com
ple
men
tary
ang
les.
Th
e co
sin
e o
f an
acu
te a
ng
le is
eq
ual
to
th
e si
ne
of
its
com
ple
men
t.
©G
lenc
oe/M
cGra
w-H
ill37
4G
lenc
oe G
eom
etry
Sin
e an
d C
osi
ne
of
An
gle
sT
he
foll
owin
g di
agra
m c
an b
e u
sed
to o
btai
n a
ppro
xim
ate
valu
es f
or t
he
sin
ean
d co
sin
e of
an
gles
fro
m 0
°to
90°
.Th
e ra
diu
s of
th
e ci
rcle
is
1.S
o,th
e si
ne
and
cosi
ne
valu
es c
an b
e re
ad d
irec
tly
from
th
e ve
rtic
al a
nd
hor
izon
tal
axes
.
Fin
d a
pp
roxi
mat
e va
lues
for
sin
40°
and
cos
40�
.Con
sid
er t
he
tria
ngl
e fo
rmed
by
the
segm
ent
mar
ked
40°
,as
illu
stra
ted
by
the
shad
ed
tria
ngl
e at
rig
ht.
sin
40°
��a c�
��0.
164 �or
0.6
4co
s 40
°�
�b c��
�0.177 �
or 0
.77
1.U
se t
he
diag
ram
abo
ve t
o co
mpl
ete
the
char
t of
val
ues
.
2.C
ompa
re t
he
sin
e an
d co
sin
e of
tw
o co
mpl
emen
tary
an
gles
(an
gles
wh
ose
sum
is
90°)
.Wh
at d
o yo
u n
otic
e?
Th
e si
ne
of
an a
ng
le is
eq
ual
to
th
e co
sin
e o
f th
e co
mp
lem
ent
of
the
ang
le.
00.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.91
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
90°
0°
10°
20°
30°
40°
50°
60°
70°
80°
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
7-4
7-4 x
°0°
10°
20°
30°
40°
50°
60°
70°
80°
90°
sin
x°
00.
170.
340.
50.
640.
770.
870.
940.
981
cos
x°
10.
980.
940.
870.
770.
640.
50.
340.
170
1 0
40°
0.64
c �
1 u
nit
x°b
� c
os x
°0.
771
a �
sin
x°
Exam
ple
Exam
ple
Answers (Lesson 7-4)