Name: ________________________________ Period: ________ Date: __________
Geometry Chapter 8 Test A
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Use special right triangles to find the value of the variable(s). If your answer is not an integer, leave it in
simplest radical form.
____
1.
6
x
60°
12
Not drawn to scale
a. 2
____
b.
c.
d.
1
2
2.
y
17
30°
x
Not drawn to scale
a. x = 17, y =
b. x = 34, y =
c. x =
d. x =
, y = 17
, y = 34
____
3. The length of the hypotenuse of a 30°-60°-90° triangle is 4. Find the perimeter. (Draw a triangle to help!)
a. 4 + 12
c. 2 + 6
b. 6 + 2
d. 12 + 4
____
4. Write the tangent ratios for
and
.
P
29
21
R
20
Q
Not drawn to scale
a.
c.
b.
d.
For questions 5 – 7 use what you know about special right triangles to find your answers.
____
5. In triangle ABC,
is a right angle and
simplest radical form.
45. Find BC. If your answer is not an integer, leave it in
C
11 ft
B
A
Not drawn to scale
a. 22 ft
____
b. 22
ft
c. 11 ft
d. 11
c. 3
d. 18
ft
6. Find the length of the hypotenuse.
45°
3 2
a. 12
____
b. 6
7. Find the lengths of the missing sides in the triangle.
y
7
45°
x
Not drawn to scale
a. x = 7, y  7 2
b.
x7 2,y=7
c.
x
7
2
, y  14 2
d.
x  14 2 , y 
7
2
Find the length of the missing side. Leave your answer in simplified radical form.
8.
9.
y
17
x
4
9
3
Not drawn to scale
8. x = ____________
9. y = ____________
10. A triangle has sides of lengths 12, 13, and 5. Is it a right triangle? Explain.
10. ________________________
___________________________
___________________________
11. A triangle has side lengths of 20 cm, 14 cm, and 16 cm. Classify it as acute, obtuse, or right.
11. _______________
12. Use what you know about special right triangles to find the length of the leg. If your answer is not an integer,
leave it in simplest radical form.
22
45°
Not drawn to scale
12. Leg =__________
13. You’re designing a square garden with a diagonal walkway that connects the southeast corner to the northwest
corner. The square garden is 8 m on each side. How long will your walkway be? Round your answer to the
nearest tenth. (Draw a picture to help!)
14.
13. _______________
For problems 14 – 16 use what you know about special right triangles to find the value of the
variable(s). If your answer is not an integer, leave it in simplest radical form.
14. Find the values of x, y, and z. Keep answers in simplified radical form.
14. x =_____________
y =_____________
z =_____________
15.
x
y
15. x =_____________
30°
2
y =_____________
Not drawn to scale
16. A conveyor belt carries supplies from the first floor to the second floor, which is 30 feet higher. The belt
makes a 60° angle with the ground. How far do the supplies travel from one end of the conveyor belt to the
other? Round your answer to the nearest foot. (Draw a picture to help!)
16. _______________
Given each figure, write the sine, cosine, and tangent ratios for  A .
B
17.
16
18.
17. _______________
_______________
B
16
7
_______________
4 10
A
9
C
C
8
A
18. _______________
_______________
Find the value of x. Round your answer to the nearest tenth.
19.
_______________
20.
7

x
x

19. x =_____________
9
Not drawn to scale
20. x =_____________
Not drawn to scale
Find the value of x to the nearest degree.
21.
23
x
12
Not drawn to scale
21. x =_____________
22. A large totem pole in the state of Washington is 100 feet tall. At a particular time of day, the totem pole casts
a 249-foot-long shadow. Find the measure of
to the nearest degree.
150 ft
A
318 ft
22. _______________
23. Find the value of w, then x. Round lengths of segments to the nearest tenth.
17

23. w =____________

x
w
x =_____________
Find the value of x. Round to the nearest tenth.
24.
25.
24. x =____________
10
x


25. x =____________
x
11
Not drawn to scale
Not drawn to scale
26.
26. x =____________
27.
x
18
18
x


27. x =____________
Not drawn to scale
Not drawn to scale
Find the value of x. Round to the nearest degree.
28.
29.
28. x =____________
16
32
18
x
29. x =____________
x
10
Not drawn to scale
Not drawn to scale
Find the value of x. Round the length to the nearest tenth.
30. A hang glider is standing at the top of a 200 meter cliff and sights his landing area at a 15 degree angle of
depression. Label the angle of depression in the diagram and then find the distance between the hang glider
and the landing area.
x
200 m
30. x =____________
Not drawn to scale
EXTRA CREDIT
The figure is drawn on centimeter grid paper. Find the perimeter of the shaded figure. Round your
answer to the nearest tenth.