Free Printable AdvMath Unit 19 - Triangle Trigonometry (Retake)

1.

Find the length of side y.

a)

22.32 cm

b)

36.5 cm

c)

76.34 cm

d)

87.76 cm

2.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

3.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

4.

Solve for a and b in the special right triangle.

a)

a = 5, b = 5

b)

a = 10, b = 10√2

c)

a = 10√2, b = 10√2

d)

a = 5√2, b = 5√2

5.

Solve for x and y in the special right triangle.

a)

x = 7, y = 7√2

b)

x = 14 y = 7√2

c)

x = 14√2 y = 7√2

d)

x = 14 y = 14√2

6.

Solve for u and v in the special right triangle.

a)

v = 9√3, u = 6√3

b)

v = 6√3 u = 9√3

c)

v = 9, u = 6√3

d)

v = 3√6, u = 6√3

7.

Solve for x and y in the special right triangle.

a)

y = 4, x = 4√3

b)

y = 4√2, x = 4√2

c)

y = 4 x = 12

d)

y = 8/√3, x = 16/√3

8.

Find the measure of the indicated angle (?) round to the nearest tenth.

a)

9.4

b)

55.2

c)

20.15

d)

19.4

9.

Solve for x. Round to the nearest tenth.

a)

44.0

b)

41.4

c)

1.2

d)

1.0

10.

Solve for x. Round to the nearest tenth.

a)

103.5

b)

4.7

c)

55.0

d)

23.4

11.

Solve for x. Round to the nearest tenth.

a)

9.8

b)

0.1

c)

0.038

d)

9.9

12.

A hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. The hawk swoops down toward the mouse at an angle of 30 degrees. What is the distance from the tree branch to the mouse?

a)

7.5 ft

b)

15 ft

c)

26 ft

d)

30 ft

13.

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is nearest to the height of the lighthouse?

a)

25 feet

b)

45 feet

c)

110 feet

d)

135 feet

14.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

65 ft

c)

74 ft

d)

87 ft

15.

Find the area of this triangle. Round your answer to the nearest tenth.

a)

89.0 units squared

b)

89.6 units squared

c)

9.2 units squared

d)

13.1 units squared

16.

From ∠C, what side is AB?

a)

Adjacent

b)

Hypotenuse

c)

Opposite

17.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.

a)

19 degrees

b)

45 degrees

c)

71 degrees

d)

138 degrees

18.

^{_{What is the secant of θ?}}

a)

8/15

b)

17/15

c)

17/8

d)

15/17

19.

^{What is the cotangent of angle C?}

a)

7/24

b)

25/24

c)

7/25

d)

24/7

20.

Which equation could be used to find the measure of one acute angle in the right triangle at the right?

a)

tanB = 14/9

b)

cosA = 9/14

c)

tanB = 9/14

d)

sinA = 9/14

21.

A ramp is being built next to a 4-inch high sidewalk. The ramps angle of inclination is 10 degrees. Estimate the length of the ramp to the nearest tenth of an inch.

a)

4.1 inches

b)

3.9 inches

c)

22.7 inches

d)

0.7 inches

22.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.

a)

19 degrees

b)

45 degrees

c)

71 degrees

d)

138 degrees

23.

Solve for the missing distance.

a)

18.9

b)

19.5

c)

47

d)

27.5

24.

a)

F

b)

G

c)

H

d)

J

25.

A 14 ft. ladder leans against the side of a house. The bottom of the ladder is 8 ft. away from the side of the house. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth.

a)

$55.2\degree$

b)

$34.8\degree$

c)

$29.7\degree$

d)

$60.3\degree$

26.

A kite is flying 78 ft above the ground, and the string is pulled taut. The angle of elevation of the kite is $65\degree.$ Find the length of the string. Round your answer to the nearest tenth.

a)

70.7 ft.

b)

36.4 ft.

c)

184.6 ft.

d)

86.1 ft.

27.

Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home on the road connecting the mall and her house. What is her total distance traveled?

a)

17 miles

b)

32 miles

c)

37 miles

d)

40 miles

28.

The slide at the playground has a 6 feet ladder on it to get to the top. The base of the slide measured on the ground is 8 feet away from the ladder. What is the length of the slide?

a)

8 feet

b)

5.29 feet

c)

10 feet

d)

14 feet

29.

The bottom of a 13-foot ladder is set into the ground 5 feet away from a wall. When the top of the ladder is leaned against the wall, what is the distance above the ground it will reach?

a)

12 feet

b)

13.9 feet

30.

FInd tanX

a)

32/40

b)

40/24

c)

32/24

d)

24/32

31.

Find sinA

a)

32/40

b)

32/24

c)

24/40

d)

24/32

32.

Find cosC

a)

16/34

b)

16/30

c)

30/34

d)

34/16

33.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

34.

What is the cosine of angle P?

a)

p/q

b)

q/r

c)

p/r

d)

r/q

35.

Find sin C

a)

21/35

b)

28/21

c)

35/28

d)

28/35

36.

Find tanZ

a)

35/21

b)

21/28

c)

35/28

d)

28/21

37.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

38.

Which trig function would help you solve for the missing angle?

a)

sine

b)

cosine

c)

tangent

d)

pythagorean theorem

39.

Which trig function would you use with this diagram?

a)

^Sin

b)

^Cos

c)

^Tan

d)

^Wha??

40.

What trigonometric ratio would be used to find the distance from the ship to the plane?

a)

sine

b)

cosine

c)

tangent

d)

inverse sine

41.

What would you use to solve for a?

a)

sin

b)

cos

c)

tan

d)

Pythagorean theorem

42.

$\cos\left(\theta\right)=?$

a)

$\frac{3}{5}$

b)

$\frac{4}{5}$

c)

$\frac{3}{4}$

d)

$\frac{4}{3}$

43.

$\tan\left(\theta\right)=?$

a)

$\frac{2}{3}$

b)

$\frac{3}{2}$

c)

$\frac{24}{8\sqrt{13}}$

d)

$\frac{16}{8\sqrt{13}}$

44.

$\csc\left(\theta\right)=?$

a)

$\frac{23}{6\sqrt{10}}$

b)

$\frac{23}{13}$

c)

$\frac{6\sqrt{10}}{23}$

d)

$\frac{\sqrt{191}}{13}$

45.

Find the measure of the indicated angle.

a)

$6^{\circ}$

b)

$20^{\circ}$

c)

$43^{\circ}$

d)

$47^{\circ}$

46.

Find the measure of the indicated side.

a)

$15.2$

b)

$11.3$

c)

$11.8$

d)

$13$

47.

What is the value of "x" in the diagram below?

a)

2.5

b)

5

c)

5√3

d)

10

48.

Find the length of side y.

a)

22.32 cm

b)

36.5 cm

c)

76.34 cm

d)

87.76 cm

49.

Which side is opposite of theta?

a)

z

b)

y

c)

x

d)

w

50.

If you are given the two sides that are not the hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

51.

$-640^{\degree}$ What quadrant is the measurement to the left in?

a)

I

b)

II

c)

III

d)

IV

52.

$-\frac{5\pi}{3}$ What quadrant is the measurement to the left in?

a)

I

b)

II

c)

III

d)

IV

53.

$\frac{10\pi}{9}$ What quadrant is the measurement to the left in?

a)

I

b)

II

c)

III

d)

IV

54.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

55.

Choose the correct ratio.

a)

cos(33)=x/14

b)

sin(33)=x/14

c)

cos(33)=14/x

d)

sin(33)=14/x

56.

what is the formula for finding the hypotnuse?

a)

a²⁺b²=c²

b)

a+b=c

c)

a-b=c

d)

c-a=c

57.

Solve for x.

a)

19.44

b)

14.87

c)

8.24

d)

30.67

58.

Solve for x

a)

9.23

b)

24.36

c)

11.82

d)

19.19

59.

Solve for x

a)

22.25

b)

11.33

c)

17.29

d)

18.01

60.

Solve for x

a)

60

b)

32.86

c)

12

d)

31.74

61.

Which is an equation of a line that is parallel to this line

a)

$y\ =\ \frac{3}{7}x\ +2$

b)

$y\ =\ \frac{7}{3}x\ +1$

c)

$y\ =\ -\frac{3}{7}x\ +4$

d)

$y\ =\ -\frac{7}{3}x\ +5$

62.

Which is an equation of a line that is perpendicular to this line

a)

$y\ =\ \frac{3}{7}x\ +2$

b)

$y\ =\ -\ \frac{7}{3}x\ +6$

c)

$y\ =\ -\ \frac{3}{7}x\ +1$

d)

$y\ =\ \frac{7}{3}x\ -2$

63.

Put this equation in slope intercept form. $y\ =\ mx\ +b$

a)

$y=\ -\frac{6}{5}x\ -3$

b)

$y=\ -\frac{6}{5}x\ +3$

c)

$y\ =\ \frac{5}{6}x\ +5$

d)

$y\ =\ -\frac{5}{6}x\ +3$

64.

What is Tan A?

a)

$\frac{15}{8}$

b)

$\frac{8}{15}$

c)

$\frac{8}{17}$

d)

$\frac{15}{17}$

65.

What is Cos B?

a)

$\frac{8}{15}$

b)

$\frac{15}{17}$

c)

$\frac{17}{8}$

d)

$\frac{8}{17}$

66.

What is Sin A

a)

$\frac{8}{15}$

b)

$\frac{15}{17}$

c)

$\frac{8}{17}$

d)

$\frac{17}{8}$

67.

How would you classify this triangle?

a)

Right scalene

b)

Right isosceles

c)

Equiangular equilateral

d)

acute scalene

68.

In this triangle the acute angles measure _____ and are _________________

a)

$30\degree,\ 60\degree\ and\ \ \ complementary$

b)

$30\degree,\ 60\degree,\ and\ \ \sup plementary$

c)

$45\degree,\ 45\degree,\ and\ \ complementary$

d)

$45\degree,\ 45\degree,\ and\ \ \ \sup plementary$

69.

We can use TOA-CAH-SOH for...

a)

Any triangle ever

b)

Right Triangles only

c)

Non-right triangles only

d)

Never

70.

What is the correct ratio?

a)

$\sin\ 29^o=\frac{91}{x}$

b)

$\cos\ 29^o=\frac{91}{x}$

c)

$\tan\ 29^o=\frac{91}{x}$

71.

What is the correct ratio?

a)

$\sin\ 40^o=\frac{w}{28}$

b)

$\tan\ 40^o=\frac{w}{28}$

c)

$\cos\ 40^o=\frac{w}{28}$

72.

What is the correct ratio?

a)

$\tan\ 37^o=\frac{x}{14}$

b)

$\sin\ 37^o=\frac{x}{14}$

c)

$\cos\ 37^o=\frac{x}{14}$

73.

What is the correct ratio?

4 lines

74.

What is the correct ratio?

4 lines

75.

What is the correct ratio?

4 lines

76.

Solve for x.

$\sin24^o=\frac{12.1}{x}$

4 lines

77.

Solve for x.

4 lines

78.

Solve for x.

4 lines

79.

What would be the next step to solve for x?

a)

Multiply both sides by cos 75

b)

Divide both sides by 75

c)

Divide both sides by cos 75

d)

Multiply both sides by 11

80.

Find the mistake.

4 lines

81.

Find the value of the missing angle.

4 lines

82.

Which trigonometric function would you use to find "h", the height of the tree?

4 lines

83.

Solve for x.

4 lines

84.

Solve for the missing distance.

4 lines

85.

The bottom of a ladder leaning against a wall is 1.5 m from the bottom of the wall. The ladder is 5.5 m long. Find how high the top of the ladder is above the ground, correct to one decimal place.

4 lines

86.

Susan is flying a kite, which gets caught in the top of a tree. Use the diagram to estimate the height of the tree.

a)

63 ft

b)

74 ft

c)

65 ft

d)

87 ft

87.

A yacht is anchored 90 feet offshore from the base of a lighthouse. The angle of elevation from the boat to the top of the lighthouse is 26 degrees. The distance between the yacht and the top of the lighthouse is about 100 feet. Which of these is closest to the height of the lighthouse?

a)

25 feet

b)

110 feet

c)

45 feet

d)

135 feet

88.

A tourist views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. How many degrees should the tourist tilt his camera down to photograph the deer? Round your answer to the nearest degree.

a)

$19^o$

b)

$71^o$

c)

$45^o$

d)

$138^o$

89.

Use the Law of Sines to solve for BC

a)

33

b)

24

c)

12

d)

29

90.

Find AB

a)

10

b)

8

c)

6.1

d)

4.9

91.

Find AC

a)

12

b)

10

c)

23

d)

14

92.

Find m<B

a)

A

b)

B

c)

C

d)

D

93.

Calculate the length of AC

a)

30

b)

24

c)

27

d)

35

94.

Calculate the length of BC

a)

24

b)

20

c)

27

d)

23

95.

What is the measure of angle A?

a)

58 degrees

b)

61 degrees

c)

78 degrees

d)

74 degrees

96.

Identify the Law of Sines

a)

$\sin^2x+\cos^2x=1$

b)

$\frac{\sin\left(A\right)}{a}=\frac{\sin\left(B\right)}{b}=\frac{\sin\left(C\right)}{c}$

c)

$\sin\left(A\right)\sin\left(B\right)\sin\left(C\right)=1$

d)

Soh Cah Toa

97.

Solve for x.

a)

24.3

b)

155.7

c)

24.3 and 155.7

d)

not possible.

98.

find X

a)

52

b)

33

c)

41

d)

29

99.

Find m<B

a)

A

b)

B

c)

C

d)

D

100.

Find BC

a)

A

b)

B

c)

C

d)

D

101.

Find BC

a)

A

b)

B

c)

C

d)

D

102.

a)

A

b)

B

c)

C

d)

D

103.

Find m<A

a)

A

b)

B

c)

C

d)

D

104.

a)

A

b)

B

c)

C

d)

D

105.

a)

A

b)

B

c)

C

d)

D

106.

Find m<C

a)

A

b)

B

c)

C

d)

D

107.

Find the area to the nearest tenth

a)

A

b)

B

c)

C

d)

D

108.

Find the area to the nearest tenth

a)

A

b)

B

c)

C

d)

D

109.

Find the area to the nearest tenth.

a)

A

b)

B

c)

C

d)

D

110.

Find the area to the nearest tenth.

a)

A

b)

B

c)

C

d)

D

111.

Find the area to the nearest tenth.

a)

A

b)

B

c)

C

d)

D

112.

Find BC

a)

A

b)

B

c)

C

d)

D

113.

Find the area to the nearest tenth.

a)

A

b)

B

c)

C

d)

D

114.

Find the length of Side BC.

a)

33

b)

24

c)

12

d)

29

115.

Find the length of side AB.

a)

10

b)

8

c)

6.1

d)

4.9

116.

What is the measure of angle A?

a)

58 degrees

b)

61 degrees

c)

78 degrees

d)

74 degrees

117.

Find the length of side AC.

a)

12

b)

10

c)

23

d)

14

118.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

119.

Which Law would you use to solve for Angle B?

a)

Law of the Jungle

b)

Law of Cosines

c)

Law of the Gravity

d)

Law of Sines

120.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

121.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

122.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

123.

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?

a)

25.23

b)

23.19

c)

22.15

d)

20.85

124.

Identify the Law of Sines

a)

Sin²x + Cos²x =1

b)

Sin(A)/a = Sin(B)/b = Sin(C)/c

c)

Sin(A)Sin(B)Sin(C) = 1

d)

Soh-Cah-Toa

125.

Two stakes are holding a small blimp in place. Stake A measures an angle of elevation of 49^o and Stake B measures an angle of elevation of 58^o. If the string attached to Stake A has a length of 148 feet, what is the length of the string attached to Stake B?

a)

152.7 feet

b)

166.3 feet

c)

157.3 feet

d)

131.7 feet

126.

Use the Law of Cosines to find the value of x. (Level 1)

a)

41.7

b)

51.7

c)

61.7

d)

71.7

127.

Jack is flying his kite. He runs 100 feet away from his house and lets out 75 feet of string. The angle of elevation from the ground to the kite is 65 degrees. How far away is the kite from the house?

a)

9285.73 ft

b)

96.36 ft

c)

24061.81 ft

d)

155.12 ft

128.

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55 degrees, and from Jamie to the bird is 63 degrees. How far away is the bird from Amanda?

a)

25.23

b)

23.19

c)

22.15

d)

20.85

129.

1.What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

130.

2. Find: a

β = 70°

c = 11

α = 40°

a)

11

b)

7.5

c)

70

d)

8

131.

3. How many triangles does the following form?

α=124°

a=1

b=2

a)

0

b)

1

c)

2

d)

Infinite

132.

4. Name the smallest angle in this triangle.

a)

∠A

b)

∠B

c)

∠C

133.

5. Find alpha

a)

53.6

b)

13.3

c)

113.1

d)

78.2

134.

6. Solve for b

α = 95^∘

β = 45^∘

a = 5

a)

3.55

b)

3.22

c)

4.12

d)

4.89

135.

7.How Many Triangles would be possible?

a)

2

b)

1

c)

0

d)

INFINITE

136.

8.Solve for x

a)

3.85

b)

4.25

c)

3.35

d)

5.65

137.

9.Solve for a.

a)

4.28

b)

8.56

c)

3.22

d)

9.45

138.

10.Solve for Beta

a)

45.2

b)

26.3

c)

36.3

d)

56.2

139.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

140.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

141.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

142.

Identify the Law of Sines

a)

Sin²x + Cos²x =1

b)

Sin(A)/a = Sin(B)/b = Sin(C)/c

c)

Sin(A)Sin(B)Sin(C) = 1

d)

y=Sin(x)

143.

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55 degrees, and from Jamie to the bird is 63 degrees. How far away, to 2 decimal places, is the bird from Amanda?

a)

25.23 ft

b)

23.19 ft

c)

22.15 ft

d)

20.85 ft

144.

Clint is building a wooden swing set for his children. Each supporting end of the swing set is to be an A-frame constructed with two 10 foot long 4-by-4s joined at a 45 degree angle. To prevent the swing set form tipping over, Clint wants to secure the base of each A-frame to concrete footings. How far apart, to three decimal places, should the footings for each A-frame be?

a)

5.461 feet

b)

9.743 feet

c)

58.579 feet

d)

7.654 feet

145.

a)

A

b)

B

c)

C

d)

D

146.

What is the area of this triangle to three decimal places?

a)

14.494 meters squared

b)

108.184 meters squared

c)

54.092 meters squared

d)

54.350 meters squared

147.

What are the possible criteria for the Law of Cosines?

a)

SSA, SSS

b)

SSA, ASA

c)

SSS, SAS

d)

AAS, ASA

148.

Find m<B to the nearest whole number.

a)

A

b)

B

c)

C

d)

D

149.