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WorksheetsRight Triangle Trigonometry
Total questions: 100
Worksheet time: 4hrs 3mins
Name
Class
Date
1.
sin 20⁰ = ?
a)
cos 70⁰
b)
sin 70⁰
c)
cos 20⁰
d)
tan 20⁰
2.
cos 40⁰ = ?
a)
sin 50⁰
b)
cos 50⁰
c)
tan 50⁰
d)
sin 40⁰
3.
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
4.
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
5.
a)
A
b)
B
c)
C
d)
D
6.
a)
A
b)
B
c)
C
d)
D
7.
a)
A
b)
B
c)
C
d)
D
8.
a)
A
b)
B
c)
C
d)
D
9.
a)
A
b)
B
c)
C
d)
D
10.
a)
A
b)
B
c)
C
d)
D
11.
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
12.
a)
A
b)
B
c)
C
d)
D
13.
Solve for the missing distance for the depth of the anchor.
a)
18.9 m
b)
19.5 m
c)
47 m
d)
27.5 m
14.
If you are given the hypotenuse and an adjacent side, which trigonometric function should you use?
a)
sine
b)
cosine
c)
tangent
d)
cotangent
15.
Find Cos(A) as a decimal rounded the the nearest ten-thousandth.
a)
.4706
b)
1.875
c)
.8824
d)
.5333
16.
Find x round to the nearest tenth.
a)
46.1
b)
4.9
c)
16.4
d)
26.9
17.
Solve for x. Round to the nearest tenth.
a)
103.5
b)
4.7
c)
55.0
d)
23.4
18.
Which is the calculator ready form to solve this problem for x?
a)
22 Tan (12)
b)
12 tan (22)
c)
tan(12) / 22
d)
22/ tan (12)
19.
Solve for x. Round to the nearest tenth.
a)
9.8
b)
0.1
c)
0.038
d)
9.9
20.
Which of the following is the calculator ready form to solve the height of the airplane?
a)
1000Sin(60)
b)
1000/Sin(60)
c)
1000Cos(60)
d)
1000/Cos(60)
21.
Jose would like to know the height of the brick building shown in the picture, if the angle of elevation is 50 degrees and he is 36 feet from the building. Which of these is the calculator ready expression to find the building height?
a)
36 Sin (50)
b)
36 Tan (50)
c)
36 Sin (50) + 6
d)
36 Tan (50) + 6
22.
Henry knows the angle of depression from the lookout and also knows from that angle it is 45 feet in the air. About how far is he from the middle of the lookout tower?
a)
30 feet
b)
35 feet
c)
38 feet
d)
54 feet
23.
Find the missing side
a)
9
b)
41
c)
6.4
d)
6.2
24.
Find h
a)
35.60
b)
35.00
c)
35.71
d)
61.03
25.
Find the length of the missing side.
a)
48 in.
b)
52 in.
c)
16 in.
d)
24 in.
26.
Do the segment lengths 15, 12, and 9 form a right triangle?
a)
Yes
b)
No
c)
Maybe
d)
Pythagoras
27.
Find the length of the missing side.
a)
17 cm
b)
22 cm
c)
15 cm
d)
13 cm
28.
The Pythagorean Theorem classifies which triangles based on their given side lengths?
a)
obtuse
b)
scalene
c)
isosceles
d)
right
e)
acute
29.
What is the opposite of squaring a number?
a)
divide
b)
multiply
c)
fractions
d)
square root
30.
a= 12, b= 35, c= ? Find c
a)
32
b)
37
c)
19
d)
20
31.
c= 97, b= 72, a=?
a)
35
b)
75
c)
65
d)
55
32.
You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?
a)
25 feet
b)
26 feet
c)
27 feet
d)
28 feet
33.
John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school?
a)
14 blocks
b)
12 blocks
c)
10 blocks
d)
8.5 blocks
34.
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
35.
A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?
a)
111.8 yards
b)
115 yards
c)
127.3 yards
d)
119 yards
36.
Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards. What is the length of the diagonal, in yards, that Tanya runs?
a)
26.5 yards
b)
10 yards
c)
50 yards
d)
46.7 yards
37.
a)
9.2 in
b)
11 in
c)
13 in
d)
9.6 in
38.
A piece of paper that Brittany has is 11 inches tall and 8 inches wide. She draws a straight line diagonally across the paper. How long is the line she drew?
a)
7.5 in
b)
12.4 in
c)
13.6 in
d)
14.3 in
39.
An airplane flies 56 miles due north and then 33 miles due east. How many miles is the plane from its starting point?
a)
65 miles
b)
89 miles
c)
45.4 miles
d)
We don't have enough information.
40.
Find the distance between these 2 points.
a)
5.8
b)
6.3
c)
8.1
d)
40
41.
Find the distance between the 2 points. Round to the nearest hundredth.
a)
3
b)
2.23
c)
2.24
d)
2.2
42.
In a computer catalog, a computer monitor is listed as being 27 inches. This distance is the diagonal distance across the screen. If the screen measures 15 inches in height, what is the actual width of the screen to the nearest inch?
a)
22 in
b)
23 in
c)
24 in
d)
25 in
43.
What is the length of side x?
a)
6.57 cm
b)
7 cm
c)
7.44 cm
d)
26.33 cm
44.
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
45.
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
46.
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
47.
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
48.
Which of the following is correct for finding the measure of angle Z?
a)
∠Z = tan-1 55/48
b)
∠Z = sin-1 48/55
c)
∠Z = cos-1 55/73
d)
∠Z = tan-1 48/73
49.
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
50.
From ∠C, what side is AB?
a)
Adjacent
b)
Hypotenuse
c)
Opposite
51.
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
52.
Use inverse trig ratios (SOH CAH TOA) to solve for the missing angle
a)
33°
b)
49°
c)
39°
d)
41°
53.
The angle of 12o is a(n)
a)
angle of elevation
b)
angle of depression
c)
neither
d)
both
54.
Is the given angle of 70 degrees, an angle of elevation or an angle of depression?
a)
Angle of Elevation
b)
Angle of Depression
c)
Neither
d)
Both
55.
Give the Ratio for SIN X
a)
opp/adj
b)
Adj/hyp
c)
Opp/hyp
d)
adj/opp
56.
Give the Ratio for TAN X
a)
Adj/Opp
b)
Opp/Adj
c)
Adj/Hyp
d)
Opp/Hyp
57.
Give the Ratio for COS X
a)
Adj/Hyp
b)
Opp/Adj
c)
Adj/Opp
d)
Opp/Hyp
58.
We can use SOH-CAH-TOA for...
a)
Any triangle ever
b)
Non-right triangles only
c)
Right Triangles only
d)
Never
59.
Find r and s.
a)
r = 9, s = 9√3
b)
r = 18, s = 9
c)
r = 9√3, s = 9
d)
r = 18, s = 9√3
60.
From a horizontal distance of 80.0 m, the angle of elevation to the top of a flagpole is 18°. Calculate the height of the flagpole to the nearest tenth of a meter.
a)
26.0 m
b)
246.2 m
c)
24.7 m
d)
258.9 m
61.
Jake built a skateboard ramp that covers a horizontal distance of 10 ft. The ramp rises a total of 3.5 ft. What angle does the ramp make with the ground? Round to the nearest degree.
a)
19 degrees
b)
20 degrees
c)
28 degrees
d)
35 degrees
62.
Spencer is going snowboarding. He rode the ski lift to the top of the mountain, which is at an altitude of 1500 feet. The angle of elevation from the bottom to the top of the mountain is 25o. What is the length of the Spencer’s run (his trip down the hill)?
a)
3216.76 feet
b)
633.93 feet
c)
699.46 feet
d)
3549.30
63.
A vertical tower is 20 m high from the horizontal ground. The angle of depression of a ball from the top of the tower is 42°. Calculate the distance, in m, of the ball from the base of the tower
a)
18.01 m
b)
29.89 m
c)
13.38 m
d)
22.21 m
64.
What is the correct ratio?
a)
sin 40 = w/28
b)
cos 40 = w/28
c)
tan 40 = w/28
d)
sin 40 = 28/w
65.
Choose the correct ratio.
a)
sin(37)=x/14
b)
cos(37)=x/14
c)
tan(37)=x/14
d)
sin(37)=14/x
66.
Set up the problem...
a)
sin X = 41/28
b)
tan X = 41/28
c)
cos X = 28/41
d)
sin X = 28/41
67.
Based on the diagram, choose all the statements that are true.
a)
b)
c)
d)
e)
68.
Jayden is on his boat riding through the Cooper River. He spots the Cooper River Bridge the horizontal distance is 420. If the bridge stands 761 feet above Jayden’s viewing point on the boat, how far is Jayden from the bridge?
a)
804.7 feet
b)
845.2 feet
c)
893.4 feet
d)
915.1 feet
e)
869.2 feet
69.
A 50 ft tall tree is casting a shadow while the sun is at an angle of elevation of 63°. To the nearest foot, how long is the tree’s shadow?
a)
25 feet
b)
56 feet
c)
98 feet
d)
110 feet
70.
From the top of a canyon, the angle of depression to the far side of the river is 52°. The angle of depression to the near side of the river is 79°. The depth of the canyon is 400 feet. To the nearest foot, how wide is the river at the bottom of the canyon?
a)
104 ft
b)
235 ft
c)
204 ft
d)
785 ft
71.
Right triangle ABC is shown below. Which equation gives the correct value for BC?
a)
b)
c)
d)
e)
Not enough information to solve BC
72.
The following diagram represents a rectangular garage door with two diagonal beams as decoration. Find the measure of x given that the horizontal length is 24 feet while the height is 10 feet.
a)
46°
b)
67°
c)
90°
d)
100°
73.
Find Tan A
a)
21/20
b)
29/20
c)
21/29
d)
20/21
74.
Find Sin C
a)
21/20
b)
20/29
c)
21/29
d)
20/21
75.
Tan C
a)
27/45
b)
36/27
c)
36/45
d)
27/36
76.
Which scenario describes the picture shown?
a)
A 5 foot ramp is 8 feet away from a building. What is the angle that the ramp makes with the ground?
b)
A 5 foot ramp leans against an 8 foot structure. What is the angle that the ramp makes with the ground?
c)
An 8 foot ramp leans
against a building 5 feet away. What angle does the ramp make with the ground?
against a building 5 feet away. What angle does the ramp make with the ground?
d)
A 5 foot man is 8 feet away from a building. What is the angle of elevation?
77.
Which scenario best represents the picture shown?
a)
You are walking towards a building that is 100 feet tall. The angle of depression from the building to you is 32 degrees. How far away are you from the building?
b)
You are walking towards a building. When you are 100 ft away, the angle of depression, from the top of the building to you is 32 degrees. How tall the is the building?
c)
You are 32 feet away from a 100 foot building. What is the angle of elevation?
d)
A 100 foot ramp makes a 32 degree angle of elevation with the ground. How far away is the ramp from the building?
78.
Which trigonometric ratio is correct?
a)
cosC= adj/hyp
b)
sinC= adj/hyp
c)
tanC= adj/hyp
d)
tanC=adj/opp
79.
Find the trig value rounded to the nearest ten-thousandth.
Tan(42°)
Tan(42°)
a)
.9004
b)
.8123
c)
88.6361
d)
42
80.
sin 20⁰ = ?
a)
cos 70⁰
b)
sin 70⁰
c)
cos 20⁰
d)
tan 20⁰
81.
cos 40⁰ = ?
a)
sin 50⁰
b)
cos 50⁰
c)
tan 50⁰
d)
sin 40⁰
82.
Which of the following is NOT a Pythagorean Triple?
a)
3, 4, 5
b)
5, 12, 13
c)
7, 14, 16
d)
8, 15, 17
83.
Which of the following IS a Pythagorean Triple?
a)
6, 8, 10
b)
10, 24, 26
c)
14, 28, 32
d)
16, 30, 34
84.
Which trigonometric ratio would you use to find ∠A?
a)
sine
b)
cosine
c)
inverse sine
d)
inverse tangent
85.
Which trigonometric ratio would you use to find ∠A?
a)
cosine
b)
tangent
c)
inverse sine
d)
inverse tangent
86.
Which trigonometric ratio would you use to find x?
a)
cosine
b)
tangent
c)
inverse cosine
d)
sine
87.
Name the angle of elevation
a)
∠R
b)
∠S
c)
∠T
d)
∠W
88.
Name the angle of depression
a)
∠R
b)
∠S
c)
∠T
d)
∠W
89.
Name the angle of depression
a)
∠F
b)
∠L
c)
∠S
d)
∠T
90.
Name the angle of elevation
a)
∠F
b)
∠L
c)
∠S
d)
∠T
91.
Name the angle of elevation
a)
∠P
b)
∠R
c)
∠W
d)
∠Z
92.
Name the angle of depression
a)
∠R
b)
∠P
c)
∠W
d)
∠Z
93.
Classify the triangle if c2 < a2 + b2
a)
acute
b)
right
c)
obtuse
94.
Classify the triangle if c2 > a2 + b2
a)
acute
b)
right
c)
obtuse
95.
Classify the triangle if c2 = a2 + b2
a)
acute
b)
right
c)
obtuse
96.
CUBS is a Rhombus.
Find BC
a)
61.6
b)
30.8
c)
27
d)
13.5
97.
A 16 foot ladder leans against a building. If the angle the ladder makes with the ground is 68°, how high up the building does the ladder reach?
a)
39.6
b)
6.0
c)
14.8
d)
13.6
98.
A pilot looks down and sees the runway at an angle of depression of 10°. If the horizontal distance between the plane and the runway is 8000 feet, what is the height of the plane?
a)
1410.6
b)
1389.2
c)
5671.3
d)
7878.5
99.
You decide to go to the city for a day of fun. You happen to be standing 30 feet away from a building that is 645 feet tall. What is your angle of elevation to the top of the building?
a)
87.3
b)
2.6
c)
79.1
d)
84.6
100.
A traffic helicopter spots two different accidents. One is east at an angle of depression of 35 degrees. The other is west at an angle of depression of 21 degrees. If the helicopter is 800 feet in the air, how far apart are the accidents?
a)
1142
b)
2084
c)
3226
d)
942
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