Name: ________________________ Class: ___________________ Date: __________
ID: A
Right Triangles Item Bank from Geo Test Bank
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. A triangle has sides of lengths 12, 14, and 19. Is it a right triangle? Explain.
c. no; 12 2 + 14 2 ≠ 19 2
a. yes; 12 2 + 14 2 ≠ 19 2
b. no; 12 2 + 14 2 = 19 2
d. yes; 12 2 + 14 2 = 19 2
2. A triangle has side lengths of10 cm, 24 cm, and 26 cm. Classify it as acute, obtuse, or right.
a. right
b. acute
c. obtuse
3. Find the length of the hypotenuse.
____
a. 12
b. 6
c. 5
d. 18
4. Find the length of the leg. If your answer is not an integer, leave it in simplest radical form.
____
a.
128
b.
8 2
c.
16
d.
2 2
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
____
5.
a.
2
b.
12 3
c.
1
1
2
d.
6 3
Name: ________________________
____
ID: A
6.
Not drawn to scale
a.
x = 10 3 , y = 30
c.
x = 30 3 , y = 10
____
b. x = 10, y = 30 3
d. x = 30, y = 10 3
7. Find the value of x and y rounded to the nearest tenth.
____
a. x = 48.1, y = 46.4
b. x = 48.1, y = 139.3
8. Write the tangent ratios for ∠Y and ∠Z.
a.
tan Y =
b.
tan Y =
6
7
; tan Z =
7
6
85
; tan Z =
7
85
6
c.
d.
x = 24.0, y = 139.3
x = 24.0, y = 46.4
c.
tan Y =
d.
tan Y =
2
7
6
; tan Z =
6
7
7
; tan Z =
85
6
85
Name: ________________________
ID: A
Find the value of x. Round your answer to the nearest tenth.
____
9.
a.
6.2 cm
b.
12.7 cm
c.
15.5 cm
d.
10.9 cm
c.
70
d.
85
Find the value of x to the nearest degree.
____ 10.
a.
30
b.
60
____ 11.
a. 67
b. 22
c. 83
d. 53
____ 12. Find the value of w, then x. Round lengths of segments to the nearest tenth.
a.
b.
w = 13.3, x = 10.2
w = 10.8, x = 6.1
c.
d.
3
w = 13.3, x = 23.6
w = 10.8, x = 16.9
Name: ________________________
ID: A
____ 13. Write the ratios for sin X and cos X.
a.
sin X =
119
, cos X =
5
b.
sin X =
119, cos X = 5
5
119
c.
sin X =
119
5
, cos X =
12
12
d.
sin X =
5
, cos X =
119
Find the value of x. Round to the nearest tenth.
____ 14.
a.
12.5
b.
10
c.
13
d.
9.7
a.
10.3
b.
31.4
c.
10.7
d.
31.8
____ 15.
4
119
5
Name: ________________________
ID: A
____ 16.
a.
52.6
b.
52.9
c.
6.2
d.
6.5
Find the value of x. Round to the nearest degree.
____ 17.
a. 41
b. 36
c. 46
d. 44
____ 18. Find the value of w and then x. Round lengths to the nearest tenth and angle measures to the nearest degree.
a.
b.
w = 7.7, x = 44
w = 6.4, x = 54
c.
d.
w = 7.7, x = 54
w = 6.4, x = 44
Find the value of x. Round the length to the nearest tenth.
____ 19.
a.
1134.3 m
b.
1151.8 m
c.
5
34.7 m
d.
203.1 m
Name: ________________________
ID: A
____ 20.
a. 15.6 yd
b. 10.4 yd
c. 9 yd
d. 31.2 yd
____ 21. An airplane over the Pacific sights an atoll at an angle of depression of 5°. At this time, the horizontal distance
from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter?
a. 403 m
b. 405 m
c. 4611 m
d. 4647 m
____ 22. To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then, with a transit
4 feet tall, measures the angle of elevation to the top of the pole to be 44°. To the nearest foot, what is the
height of the pole?
a. 145 ft
b. 149 ft
c. 135 ft
d. 139 ft
____ 23. A spotlight is mounted on a wall 7.4 feet above a security desk in an office building. It is used to light an
entrance door 9.3 feet from the desk. To the nearest degree, what is the angle of depression from the spotlight to
the entrance door?
a. 39°
b. 51°
c. 53°
d. 37°
Short Answer
24. A highway makes an angle of6° with the horizontal. This angle is maintained for a horizontal distance of8
miles.
a. Draw and label a diagram to represent this situation.
b. To the nearest hundredth of a mile, how high does the highway rise in this8-mile section?
Show the steps you use to find the distance.
25. A forest ranger spots a fire from a 21-foot tower. The angle of depression from the tower to the fire is12°.
Draw a diagram to represent this situation.
a.
To the nearest foot, how far is the fire from the base of the tower? Show the steps you
b.
use to find the solution.
6