9.5 trigonometric ratios how are trigonometric ratios used to find missing sides of right triangles?
TRANSCRIPT
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9.5 Trigonometric ratios
How are trigonometric ratios used to find missing sides of right
triangles?
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• Trig ratio- ratio of the lengths of two sides of a right Δ. Used to find missing side lengths when only 1 length is known.
• Always round to four decimal places
38°
12
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3 basic trig ratios• Sine (sin)
• Cosine (cos)
• Tangent (tan)
• Sin
• Cos
• Tan
hypot
sideOpp .
hypot
sideadj .
adj
opp
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Just remember Chief…
SOH CAH TOAine
ppos i te
ypotenus
osine
dj acent
ypotenus
angent
ppos i te
dj acent
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Ratios of s A and BA B
c
aAsin
c
bAcos
b
aAtan
c
bB sin
c
aB cos
a
bB tan
A
BC a
bc
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Ex: Find sin, cos, & tan of A & B. A
sin A= 12/13 = .9231
cos A= 5/13 = .3846
tan A= 12/5 = 2.4
B
sin B= 5/13 = .3846
cos B= 12/13 = .9231
tan B= 5/12 = .4167
C
A
B
13
12
5
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Example
30
60__
__
1
2
A
BC
3
sin A= ½ or .5
sin 30= .5
Find sin A and sin 30o.
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Example
45
45__
__A
BC1
12
7071.2
2or
2
1 sin B
sin 45o =.7071
Find sin B and sin 45o.
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• Using your calculator find
tan 23
sin 72
cos 44
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Assignment
Trigonometric Ratios WS #1-24
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Use trig to solve for n.
35
8
m
n
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Use trig to solve for m.
35
8
m
n
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Use trig to find t.
72
13
z
t
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Use trig to find z.
72
13
z
t
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Angle of elevation
ground
angl
e of
ele
vatio
n
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ExampleFind the height of the tree
48o
100 ft
__
__
h
You are given the adj side & finding the opp side.
Use tangent!!
tan 48o = h/100
111.06 = hAbout 111 ft
100 tan 48o = h
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Example
100ft
30o
d
__
__
Have opp side need hypot
Use sine!!
do 1000
30sin .5d=1000
d=2000 ftd
10005.
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Assignment
Trigonometry WSTrigonometry WS#1-18#1-18