basic practice final exam #1 - m2 mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/52631585/... ·...

Basic Practice Final Exam #1

Class Name : GEOMETRY RETAKE Instructor Name : Mr. Beckey

Student Name : _____________________ Instructor Note :

1. Classify the segment in each part below.Only use the information given in the figure. Do not assume measures are equal unless the markings indicate they are.

2. Consider in the figure below.

(a) Select all that describe .G I

F

G

HI

Perpendicular bisector of FH

Angle bisector of ∠G

Median of FGH

Altitude of FGH

None of the above

(b) Select all that describe .ZV

X

Y

Z

V

Perpendicular bisector of XY

Angle bisector of ∠Z

Median of XYZ

Altitude of XYZ

None of the above

(c) Select all that describe .AD

A

B

C

D

Perpendicular bisector of BC

Angle bisector of ∠A

Median of ABC

Altitude of ABC

None of the above

© 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.Bas i c Pr ac t i ce F i nal Exam #1 Page 1 / 50

2. Consider in the figure below.

The perpendicular bisectors of its sides are , , and . They meet at a single point .

(In other words, is the circumcenter of .)

Suppose , , and .

Find , , and .Note that the figure is not drawn to scale.

_____

_____

_____

3. The angle bisectors of are They meet at a single point

XYZ

TS US VS S

S XYZ

=VS 80 =YZ 86 =ZS 116XS UZ VY

=XS

=UZ

=VY

X

Y

ZT

UVS


3. The angle bisectors of are , , and . They meet at a single point .

(In other words, is the incenter of .)

Suppose , , , and .Find the following measures.Note that the figure is not drawn to scale.

_____

_____

_____

4. The medians of are and They meet at a single point

ABC AV BV CV V

V ABC=SV 6 =BV 19 =m∠ SBT 34 ° =m∠ UCV 22 °

=UV

=m∠ UCT ° =m∠ UAV °

A

B

C

S T

U

V


4. The medians of are , , and . They meet at a single point .

(In other words, is the centroid of .)

Suppose , , and .Find the following lengths.Note that the figure is not drawn to scale.

_____

_____

_____

5. In the figure below, points and are the midpoints of the

PQR PT QU RS V

V PQR=QU 21 =PV 18 =VS 7

=RS

=QV

=VT

P

Q

R

S T

U

V


5. In the figure below, points , , and are the midpoints of the sides of .

Suppose , , and .Find the following lengths.

_____

_____

_____

6. Use the given information to prove the following theorem.

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of thesegment.

Given: is the bisector of

Prove:

7. Classify the segment in each part below.

S T U PQR

=QR 28 =SU 50 =PR 96

=PQ

=TU

=PT

PX ⊥ WY=WP YP

P Q

R

S

T

U

P

WY Xl




(a) Select all that describe .KM

J

K

LM

Perpendicular bisector of JL

Angle bisector of ∠K

Median of JKL

Altitude of JKL

None of the above

(b) Select all that describe .CD

A

B

C

D

Perpendicular bisector of AB

Angle bisector of ∠C

Median of ABC

Altitude of ABC

None of the above

(c) Select all that describe .ST

P

Q

R

S

T

Perpendicular bisector of QR

Angle bisector of ∠P

Median of PQR

Altitude of PQR

None of the above




(a) Select all that describe .AD

A

B

C

D



Median of ABC

Altitude of ABC

None of the above

(b) Select all that describe .IO

F

G

H

I

O

Perpendicular bisector of FG

Angle bisector of ∠H

Median of FGH

Altitude of FGH

None of the above

(c) Select all that describe .JM

J

K

L

M

Perpendicular bisector of KL

Angle bisector of ∠ J

Median of JKL

Altitude of JKL

None of the above



10. For the following right triangle, find the side length

(a) Select all that describe .MN

J

K

L

M

N



Median of JKL

Altitude of JKL

None of the above


A

B

C

D



Median of ABC

Altitude of ABC

None of the above

(c) Select all that describe .QS

P

Q

RS

Perpendicular bisector of PR

Angle bisector of ∠Q

Median of PQR

Altitude of PQR

None of the above


10. For the following right triangle, find the side length .

11. For the following right triangle, find the side length . Round your answer to the nearest hundredth.

12. Which pairs of figures are congruent? Which pairs are similar?

x

x

9

12

x

x

10

12


12. Which pairs of figures are congruent? Which pairs are similar?

13.

(The triangles are not drawn to scale.)

14. The two triangles below are similar.

Congruent? Yes No Congruent? Yes No

Similar? Yes No Similar? Yes No



A

B

C D

E

F

? 8

7 42

24 48

and are similar. Find the missing side length.ΔABC ΔDEF


14. The two triangles below are similar.

Also, and as shown below.

Find , , and .

Assume the triangles are accurately drawn.

____

____

____

15. The quadrilaterals and are similar.

=m∠ E 50 ° =m∠ G 105 °m∠ J m∠ K m∠ L

m∠ J = °m∠ K = °m∠ L = °

F

E

G

50°

105°

J

L

K


15. The quadrilaterals and are similar.

Find the length of .

16. Find the length .

17. A pole that is tall casts a shadow that is long. At the same time, a nearby tower casts a

shadow that is long. How tall is the tower? Round your answer to the nearest meter.

18. In , . Given that find .

ABCD PQRS

x RS

x

2.7 m 1.64 m38.75 m

D5

3

2

4B A

C

S

9

x

3.6

7.2Q P

R

x

32

5


18. In , . Given that , , and , find .

19. Find the value of each variable.Simplify your answers as much as possible.

_____

_____

20. Decide whether the triangles are similar. If they are, write a similarity statement and state the reason justifying

JKL JK MN =LM 12 =NK 28 =LN 16 MJ

=x

=y

L

N

J K

M

4x

23

4

8

9

y


20. Decide whether the triangles are similar. If they are, write a similarity statement and state the reason justifyingthe similarity.

If necessary, you may learn what the markings on a figure indicate.

Not similar or not necessarily similar

Similar: ___, by the

Angle-Angle (AA) Similarity Property Side-Side-Side (SSS) Similarity Property

Side-Angle-Side (SAS) Similarity Property









21. Use the given information to prove that .

Given:

Prove:

22. Use the given information to complete the proof of the following theorem.

XYZ ~

ABC ~

JKL ~

DEF ~ GHF

=DFGF

EF

HF

DEF ~ GHF

Y ZN

X

M

75

8

6

9

7

C

F

A E

B

D

40°

15°

125 °125 °

L

I

K

G

J

H

D

E

F

G

H


22. Use the given information to complete the proof of the following theorem.

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Given:

Prove:

=RTTP

QS

SP

RQ TSStatement Reason

1 =R T

TP

QS

SPGiven

2 =+R T

TP1 +

QS

SP1 _______________

3 =+R T

TP

TP

TP+

QS

SP

SP

SPFraction Algebra 2

4 =+R T TPTP

+QS SPSP

Fraction Algebra 3

5 =RP +R T Segment Addition Property

6 =QP +QS Segment Addition Property

7 =RP

TP

QP

SP_______________

8 =~∠P ∠P _______________

9 ~PQR SAS Similarity Property 7 8

10 =~∠PRQ ∠P T S _______________

11 RQ _______________

Line(s) Used

S

T

P

Q

R


23. In the figure below, and are perpendicular.

Complete the following.

VP PZ

xx

yy

O

V

W P Q

Z


24. In a scale drawing of a house, inch represents feet.

(a) Find the slope of and the slope of .VP PZ

slope of :VPVW

WP−VW

WP−WP

VW

WP

VW

slope of :PZ −PQ

QZ

PQ

QZ−

QZ

PQ

QZ

PQ

(b) It can be shown that .

Based on this, choose the ratio that is equal to .

VWP ~ PQZVW

WP

PQ

QZ

QZ

PQ

PZ

QZ

PQ

PZ

(c) Using the results above, choose the correct statement below.

slope of slope of VP = PZ

slope of slope of VP · PZ = 1

slope of slope of VP = − PZ

slope of slope of VP · PZ = − 1

(d) The result in part (c) is an example of the following rule for any two non-vertical perpendicular lines.

The slopes of the two lines are the same.

The slopes of the two lines are reciprocals.

The slopes of the two lines are negative reciprocals.

The slopes of the two lines are opposites.

1 5 © 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.Bas i c Pr ac t i ce F i nal Exam #1 Page 17 / 50

24. In a scale drawing of a house, inch represents feet.

Scale

Answer the following.

(a) The length of the real house is feet. What is the length ofthe house in the scale drawing?

____ inches

(b) In the scale drawing, the height of the house is inches. Whatis the height of the real house?

____ feet

25. The table below gives the dimensions of a painting and a scale drawing of the painting.

Find the scale factor of the drawing to the real painting. Write your answer as a fraction in simplest form.

Painting Drawing

Length (inches)

Width (inches)

26. A tall building casts a shadow. The distance from the top of the building to the tip of the shadow is

1 5

:1 in 5 ft

35

8

21 7

18 6

28 m © 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.Bas i c Pr ac t i ce F i nal Exam #1 Page 18 / 50

26. A - tall building casts a shadow. The distance from the top of the building to the tip of the shadow is

. Find the length of the shadow. If necessary, round your answer to the nearest tenth.

27. Determine whether a triangle with the given side lengths is a right triangle.

Side lengths Right triangle Not a right triangleNot enoughinformation

, ,

, ,

, ,

, ,

28. Below are two triangles with their side lengths shown.

28 m37 m

10 24 26

24 32 40

6 7 9

22 29 36

?

28

37


28. Below are two triangles with their side lengths shown.

Answer the questions about each triangle.

Compute the sum of the squares of theshorter lengths.

______

Compute the square of the longestlength.

______

What kind of triangle is it?

Acute triangle

Right triangle

Obtuse triangle

Compute the sum of the squares of theshorter lengths.

______

Compute the square of the longestlength.

______


Acute triangle

Right triangle

Obtuse triangle

29. In the figure below, there are three right trangles. Complete the following.

30. In the figure below, find the exact value of (Do not approximate your answer.)

+6 2 8 2 =

10 2 =

+6 2 15 2 =

18 2 =

A B

C

D

(a) Write a similiarity statement relating the three right triangles.

~DCB ~

(b) Complete each proportion.

=DB

CB

CB=

DA

DC DB

6

108

15

186


30. In the figure below, find the exact value of . (Do not approximate your answer.)

31. In the figure below, .

Fill in the following blanks using the lengths , , , , and .Part 1: Complete the proportions.

Part 2: Use the method of cross products to rewrite the equations in Part 1.

__ __Part 3: Use Part 2 to fill in the blanks.

__ __Part 4: Factor the right-hand side of Part 3.

__ __Part 5: Use the Segment Addition Property.

__Part 6: Use Part 5 to rewrite the equation in Part 4.

__Part 7: Simplify.

__

32. For the right triangles below, find the values of the side lengths and

y

ADC ~ CDB ~ ACB

a b c x y

=cb

b =

c

a

a

=b2 ·c =a2 ·c

=+a2 b2 ·c ·+c

=+a2 b2 c +

=+x y

=+a2 b2 c

=+a2 b2 2

4

y

5

B A

C

D

ba

c

x y


32. For the right triangles below, find the values of the side lengths and .

Round your answers to the nearest tenth.

33. For the right triangles below, find the exact values of the side lengths and .

If necessary, write your responses in simplified radical form.

34. A right triangle has side lengths as shown below.

d c

a b

5 12 13

60°

30°

d

7

45°

45°

6c

45°

45°

a

3

60°

30°

4

b


34. A right triangle has side lengths , , and as shown below.

Use these lengths to find , , and .

35. Use a calculator to evaluate each expression.Round your answers to the nearest hundredth.

_______

_______

_______

36. The figure below is a right triangle with side lengths and

5 12 13cos B tan B sin B

cos 79 ° =

tan 28 ° =

sin 49 ° =

B

AC

5

12

13


36. The figure below is a right triangle with side lengths , , and .

Suppose that does not equal .

Complete the following.

Part 1: Use , , and to fill in the blanks.Make sure to use the appropriate upper-case or lower-case letters.

Part 2: In , and are

- neither complementary nor supplementary.- supplementary.- complementary.

Part 3: Select all of the true statements.

None of the above is true.

Part 4: Fill in the blank.

______

37. Solve for in the triangle. Round your answer to the nearest tenth.

t u v

m∠ T m∠ U

t u v

=sin T =cos U

=sin U =cos T

TUV ∠ T ∠ U

=cos T sin U=sin T sin U=sin T cos U=cos T cos U

=sin 62 ° cos °

T

U

V

vt

u


37. Solve for in the triangle. Round your answer to the nearest tenth.

38. Solve the right triangle.


39. If the sun is above the horizon, find the length of the shadow cast by a building tall. Round your

x

59 ° 51 ft

47°x

14

46°

B

c

b

19


39. If the sun is above the horizon, find the length of the shadow cast by a building tall. Round youranswer to the nearest tenth.

40. A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment, he is

located meters from one entrance of the tunnel, at an angle of to the perpendicular. Also according to

his equipment, he is meters from the other entrance of the tunnel, at an angle of to the perpendicular.Based on these measurements, find the length of the entire tunnel.

Do not round any intermediate computations. Round your answer to the nearest tenth.

Note that the figure below is not drawn to scale.

41. Find . Round your answer to the nearest tenth of a degree.

59 ° 51 ft

54 56 °31 13 °

59°?

51

56° 13°54 meters

31 meters


41. Find . Round your answer to the nearest tenth of a degree.

42. A plane is north and east of an airport. Find , the angle the pilot should turn in order to flydirectly to the airport. Round your answer to the nearest tenth of a degree.

43. Consider a triangle like the one below. Suppose that and (The figure is

x

111 mi 167 mi x

=122 ° =27 ° =9

x

17

11

A i r p o r t

x

N

S

W E

167

111


43. Consider a triangle like the one below. Suppose that , , and . (The figure isnot drawn to scale.) Solve the triangle.


44. Consider a triangle like the one below. Suppose that , , and . (The figure isnot drawn to scale.) Solve the triangle.

Carry your intermediate computations to at least four decimal places, and round your answers to the nearesttenth.

45. As shown in the figure below, Juan is standing feet from the base of a leaning tree. The tree is growing at

ABC =A 122 ° =B 27 ° =a 9

ABC =a 12 =b 15 =A 27 °

94

A

BC

cb

a

A

BC

cb

a


45. As shown in the figure below, Juan is standing feet from the base of a leaning tree. The tree is growing at

an angle of with respect to the ground. The angle of elevation from where Juan is standing to the top of the

tree is . Find the distance, , from the bottom to the top of the tree. Round your answer to the nearest tenthof a foot.

46. The side lengths for below are , , and

The height of is .

Fill in the blanks using the lengths , , , and to derive the Law of Sines.Make sure to use the appropriate upper-case or lower-case letters.

47. Consider a triangle like the one below. Suppose that and (The figure is not

9488 °

31 ° x

ABC a b c

ABC h

a b c h

c

C

a

Ab

B

h

Part 1: Use trigonometry to fill in the blanks.

=sinB =and sinC

Part 2: Rewrite the equations from Part 1.

=h =⋅ sinB and h ⋅ sinC

Part 3: Use the equations from Part 2 to write an equation

relating and .sin B sin C

=⋅ sinB ⋅ sinC

Part 4: Rewrite the equation from Part 3.

=sinB sinC

=65 =27 =71

31°94 ft

88°

x


47. Consider a triangle like the one below. Suppose that , , and . (The figure is notdrawn to scale.) Solve the triangle.

Carry your intermediate computations to at least four decimal places, and round your answers to the nearesttenth.

48. Chau is flying two kites. He has feet of string out to one kite and feet out to the other kite. The

angle between the strings is as shown in the figure below. Find the distance between the kites.

Carry your intermediate computations to at least four decimal places.Round your answer to the nearest tenth of a foot.

49. The side lengths for are and

ABC =a 65 =b 27 =c 71

103 11232 °

A

BC

cb

a

32 °103 ft

112 ft


49. The side lengths for are , , and

The height of the triangle is , and .

Complete the steps below to prove the Law of Cosines.

When filling in the blanks, you may use the letters , , , , and

Part 1: Use the Pythagorean Theorem to find .


Part 3: Use the answer from Part 2 to fill in the blanks.

__ __ __

Part 4: Use the answers from Parts 1 and 3 to fill in the blanks.

__ __ __ __

Part 5: Use trigonometry to fill in the blank.

__


__ __ __ __

ABC a b c

h =AD x

a b c x h

b2

=b2 −c2 a2 =b2 −c2 x2

=b2 +−a x 2 h2 =b2 +x2 h2

a2

=a2 +−b x 2 h2 =a2 −c2 x2

=a2 +−c x 2 h2 =a2 −c2 b2

=a2 +x2 +h2 −2 ·2 ·

=a2 +2 −2 ·2 ·

=x cos A

=a2 +2 −2 ·2 · cos A

1

B

b

C

c

A

aD

hx


50. For the figure below, do a dilation centered at the origin with a scale factor of .

Then, give the endpoints for both the original figure and the final figure.

Endpoints of original figure:

Left: ____ ____ Right: ____ ____

Endpoints of final figure:

Left: ____ ____ Right: ____ ____

12

Dilation

, ,

, ,

2

xx

2 4 6 8 10 12 14 16 18 20

yy

2

4

6

8

10

12

14

16

18

20

0


51. Draw the image of the following figure after a dilation centered at the origin with a scale factor of .23

xx

2 4 6 8 10 12 14 16 18

yy

2

4

6

8

10

12

14

16

18


Basic Practice Final Exam #1 Answers for class GEOMETRYRETAKE

1.

2.

3.

(a) Select all that describe .G I

F

G

HI

Perpendicular bisector of FH

Angle bisector of ∠G

Median of FGH

Altitude of FGH

None of the above

(b) Select all that describe .ZV

X

Y

Z

V

Perpendicular bisector of XY

Angle bisector of ∠Z

Median of XYZ

Altitude of XYZ

None of the above

(c) Select all that describe .AD

A

B

C

D



Median of ABC

Altitude of ABC

None of the above

=XS 116

=UZ 43

=VY 84


3.

4.

5.

6.

7.

UV =6

m∠ UCT =44 °m∠ UAV =51 °

RS =21

QV =14

VT =9

=PQ 100

=TU 48

=PT 50

Statement Reason Line(s) Used

1 is the ⊥ bisector ofP X W Y Given

2 =~W X Y X Definition of Perpendicular Bisector 1

3 is a right angle∠ W X P Definition of Perpendicular Bisector 1

4 is a right angle∠ Y X P Definition of Perpendicular Bisector 1

5 =~∠ W X P ∠ Y X P All right angles are =~ 3 4

6 =~P X P X Reflexive Property

7 =~W X P Y X P SAS Congruence Property 2 5 6

8 =~W P Y P CPCTC Property 7

9 =W P Y P Definition of Congruent Segments 8


7.

8.

(a) Select all that describe .KM

J

K

LM

Perpendicular bisector of JL

Angle bisector of ∠K

Median of JKL

Altitude of JKL

None of the above


A

B

C

D



Median of ABC

Altitude of ABC

None of the above

(c) Select all that describe .ST

P

Q

R

S

T

Perpendicular bisector of QR

Angle bisector of ∠P

Median of PQR

Altitude of PQR

None of the above


8.

9.

(a) Select all that describe .AD

A

B

C

D



Median of ABC

Altitude of ABC

None of the above

(b) Select all that describe .IO

F

G

H

I

O

Perpendicular bisector of FG

Angle bisector of ∠H

Median of FGH

Altitude of FGH

None of the above

(c) Select all that describe .JM

J

K

L

M



Median of JKL

Altitude of JKL

None of the above


9.

10.

11.

12.

(a) Select all that describe .MN

J

K

L

M

N



Median of JKL

Altitude of JKL

None of the above


A

B

C

D



Median of ABC

Altitude of ABC

None of the above

(c) Select all that describe .QS

P

Q

RS

Perpendicular bisector of PR

Angle bisector of ∠Q

Median of PQR

Altitude of PQR

None of the above

15

6.63


12.

13.

14.

15.

16.

17.

18.





4

m∠ J =25 °m∠ K =105 °m∠ L =50 °

=x 5.4

7.5

64 m

=21 © 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.Bas i c Pr ac t i ce F i nal Exam #1 Page 39 / 50

18.

19.

20. Not similar or not necessarily similar









Similar: , by the



21.

22.

=MJ 21

=x 6=y 3

XYZ ~

ABC ~

JKL ~ IGH

Statement Reason Line(s) Used

1 =D F

G F

E F

H FGiven

2 =~∠ D F E ∠ G F H Vertical Angles Property

3 ~D E F G H F SAS Similarity Property 1 2

Y ZN

X

M

75

8

6

9

7

C

F

A E

B

D

40°

15°

125 °125 °

L

I

K

G

J

H


22.

23.

Statement Reason

1 =R T

TP

QS

SPGiven

2 =+R T

TP1 +

QS

SP1 Addition and Subtraction Properties 1

3 =+R T

TP

TP

TP+

QS

SP

SP

SPFraction Algebra 2

4 =+R T TPTP

+QS SPSP

Fraction Algebra 3

5 =RP +R T TP Segment Addition Property

6 =QP +QS SP Segment Addition Property

7 =RP

TP

QP

SPSubstitution Property (Using 3 lines) 4 5 6

8 =~∠P ∠P Reflexive Property

9 ~PQR P ST SAS Similarity Property 7 8

10 =~∠PRQ ∠P T S Corr. s of similar triangles are ∠ =~ 9

11 RQ TS If corr. s , then lines ∠ =~ 10

Line(s) Used


23.

24.

(a) The length of the real house is feet. What is the length ofthe house in the scale drawing?

inches

(b) In the scale drawing, the height of the house is inches. Whatis the height of the real house?

feet

(a) Find the slope of and the slope of .VP PZ

slope of :VPVW

WP−VW

WP−WP

VW

WP

VW

slope of :PZ −PQ

QZ

PQ

QZ−

QZ

PQ

QZ

PQ

(b) It can be shown that .

Based on this, choose the ratio that is equal to .

VWP ~ PQZVW

WP

PQ

QZ

QZ

PQ

PZ

QZ

PQ

PZ

(c) Using the results above, choose the correct statement below.

slope of slope of VP = PZ

slope of slope of VP · PZ = 1

slope of slope of VP = − PZ

slope of slope of VP · PZ = − 1

(d) The result in part (c) is an example of the following rule for any two non-vertical perpendicular lines.

The slopes of the two lines are the same.

The slopes of the two lines are reciprocals.

The slopes of the two lines are negative reciprocals.

The slopes of the two lines are opposites.

35

7

8

40

1 © 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.Bas i c Pr ac t i ce F i nal Exam #1 Page 42 / 50

25. Scale factor:

26.

27.

Side lengths Right triangle Not a right triangleNot enoughinformation

, ,

, ,

, ,

, ,

28.

13

24.2 m

10 24 26

24 32 40

6 7 9

22 29 36


28.

Compute the sum of the squares of the shorterlengths.

Compute the square of the longest length.


Acute triangle

Right triangle

Obtuse triangle

Compute the sum of the squares of the shorterlengths.

Compute the square of the longest length.


Acute triangle

Right triangle

Obtuse triangle

29.

30.

31.

+6 2 8 2 = 100

10 2 = 100

+6 2 15 2 = 261

18 2 = 324

A B

C

D

(a) Write a similiarity statement relating the three right triangles.

~DCB ~CAB DAC

(b) Complete each proportion.

=DB

CB

CB

AB=

DA

DC

DC

DB

=y165

6

108

15

186


31.

Fill in the following blanks using the lengths , , , , and .Part 1: Complete the proportions.

Part 2: Use the method of cross products to rewrite the equations in Part 1.

Part 3: Use Part 2 to fill in the blanks.

Part 4: Factor the right-hand side of Part 3.

Part 5: Use the Segment Addition Property.

Part 6: Use Part 5 to rewrite the equation in Part 4.

Part 7: Simplify.

32.

33.

34.

a b c x y

=cb

b

y=c

a

a

x

=b2 ·c y =a2 ·c x

=+a2 b2 +·c x ·c y

=+a2 b2 c +x y

=+x y c

=+a2 b2 c c

=+a2 b2 c2

=d 4.0=c 8.5

=a3 2

2=b 4 3

B A

C

D

ba

c

x y


34.

35.

36.

Part 1: Use , , and to fill in the blanks.Make sure to use the appropriate upper-case or lower-case letters.

Part 2: In , and are

- complementary.

Part 3: Select all of the true statements.

None of the above is true.

Part 4: Fill in the blank.

37.

cos B =5

13

tan B =125

sin B =1213

cos 79 ° =0.19

tan 28 ° =0.53

sin 49 ° =0.75

t u v

=sin Tt

v=cos U

t

v

=sin Uu

v=cos Tu

v

TUV ∠ T ∠ U

=cos T sin U=sin T sin U=sin T cos U=cos T cos U

=sin 62 ° cos 28 °

=9.5 © 2019 M cGr aw - H i l l Educat i on. Al l R i ghts R eser ved.Bas i c Pr ac t i ce F i nal Exam #1 Page 46 / 50

37.

38.

39.

40. meters

41.

42.

43. , ,

44. , , ,

or , ,

45. feet

46.

=x 9.5

=B 44 °=b 18.3=c 26.4

30.6 ft

51.7

=x 57.1 °

=x 33.6 °

=C 31 ° =b 4.8 =c 5.5

=B 34.6 ° =C 118.4 ° =c 23.2=B 145.4 ° =C 7.6 ° =c 3.5

55.4


46.

47. , ,

48. feet

49.

c

C

a

Ab

B

h

Part 1: Use trigonometry to fill in the blanks.

=sinB =h

cand sinC

h

b

Part 2: Rewrite the equations from Part 1.

=h =⋅c sinB and h ⋅b sinC

Part 3: Use the equations from Part 2 to write an equation

relating and .sin B sin C

=⋅c sinB ⋅b sinC

Part 4: Rewrite the equation from Part 3.

=sinB

b

sinC

c

=A 66.2 ° =B 22.3 ° =C 91.4 °

59.9


49.



Part 3: Use the answer from Part 2 to fill in the blanks.


Part 5: Use trigonometry to fill in the blank.


50.

b2

=b2 −c2 a2 =b2 −c2 x2

=b2 +−a x 2 h2 =b2 +x2 h2

a2

=a2 +−b x 2 h2 =a2 −c2 x2

=a2 +−c x 2 h2 =a2 −c2 b2

=a2 +x2 +h2 −c2 ·2 ·c x

=a2 +b2 −c2 ·2 ·c x

=x b cos A

=a2 +b2 −c2 ·2 ·c b cos A

B

b

C

c

A

aD

hx


50.

Endpoints of original figure:

Left: Right:

Endpoints of final figure:

Left: Right:

51.

Dilation

, 4 8 , 6 4

, 2 4 , 3 2

xx

2 4 6 8 10 12 14 16 18 20

yy

2

4

6

8

10

12

14

16

18

20

0

xx

2 4 6 8 10 12 14 16 18

yy

2

4

6

8

10

12

14

16

18


basic practice final exam #1 - m2 mathdavidbeckeyeipbcc.weebly.com/uploads/5/2/6/3/52631585/... ·...

Documents