GPS Precalculus: Worksheet 5 - Trigonometry
Name __________________________________
mA ?
1
c. cos (0.8)
1. Which expression can be used to find
tan 1 (0.75)
4
3
3
5
b. sin 1  
d. tan 1  
2. Which expression is NOT equivalent to cos 60 ?
a.
5
3
1
2
c.
4
sin 60
tan 60
1
2
d. cos 1  
b. sin 30
3. In the figure below, if sin  
cos  and tan  ?
5
, what are
13
4. In the figure below, sin   0.7
B
21
θ
θ
a.
A
C
A
What is the length of AC ?
5. Approximately how tall is the
streetlight?
6. Right triangle ABC is pictured below
B
10.6
32
C
A
8.2
Which equation give the correct value for BC?
BC
8.2
BC
b. cos 32 
10.6
8.2
c. tan 58 
BC
BC
d. sin 58 
10.6
a.
20 ft
sin 32 
7. A surveyor 50 meters from the base of a cliff measures the angle of elevation to the top of the cliff is 72ᵒ.
What is the height of the cliff? Round to the nearest meter.
8. Grand Canyon Problem: From a point on the North Rim of the Grand Canyon, a surveyor measures an angle
of depression of 1ᵒ to a point on the South Rim. From an aerial photograph, he determines that the
horizontal distance between the two points is 10 miles. How many feet is the South Rim below the North
Rim to the nearest foot? (Note: 1 mile = 5280 feet)
9. At a point 125 feet from the base of a building, the angle of elevation to the third floor is 22ᵒ and to the ninth
floor is 53ᵒ. How much higher is the 9th floor than the 3rd floor?
11. Which ratio is equivalent to tan x
Use the triangle below for questions 10 and 11.
a.
x
25 yd
7 yd
y
24 yd
b.
c.
z
d.
10. Which ratio is equivalent to sin z?
a.
b.
c.
d.
7
24
7
25
24
25
25
7
7
24
7
25
24
25
24
7
12. What is the length of the altitude FH of
equilateral triangle EFG below?
(HINT: Find the angle measures first)
F
8
G
E
H
13. If RSTW is a rhombus, what is the area of
WXT?
R
FGH is similar to
KLM. Use these
triangles for questions 15 – 17
L
W
12
X
G
60
S
5
3
T
F
H
4
K
a. 18 3
15. Which of the following must be true?
a. tan G = tan L
b. tan G = tan M
c. sin H = tan L
d. sin H = tan M
b. 36 3
c. 36
d. 48
16. If sin G 
4
, then which of the following
5
must also be true?
14. In rectangle JKLM below, what is the length
of diagonal KM ?
L
K
5
60
J
M
4
5
4
b. sin K 
5
4
c. sin M 
5
4
d. sin L 
5
a.
sin H 
17. If sin H 
3
, then which of the following
5
must be also be true?
3
5
3
b. sin L 
5
3
c. cos L 
5
3
d. cos M 
5
a.
sin K 
M
18. Find the diagonal length
20. Find the missing value(s)
L
K
58ᵒ
30
10 cm
___
J
12
M
21. Find the missing value(s)
19. Given the diagonal of a square of 5 10 ,
find the side length.
3 2
____
_____
22. Find the missing value(s)
____
9
____
60ᵒ