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SOHCAHTOA Practice
1 – 3: For the triangle, write the sine, cosine, and tangent ratios in simplest form of X and Z.
1. sin X = _____
Z
sin Z = _____
15
2. cos X = _____
cos Z = _____
X
3. tan X = _____
9
Y
12
tan Z = _____
4 – 6: Find the sine, cosine, and tangent of both acute angles of the right triangle as reduced fractions.
4. sin P = _____
sin R = _____
P
8
5. cos P = _____
6. tan P = _____
cos R = _____
Q
R
15
tan R = _____
7 – 9: Find the sine, cosine, and tangent of both acute angles of the right triangle as simplified fractions.
Remember to rationalize denominators.
7. sin D  _____
sin F  _____
D
8. cos D  _____
cos F  _____
5
9. tan D  _____
tan F  _____
E
8
F
10 – 12: Find the indicated trigonometric ratio as a fraction and then as a decimal rounded to four decimals.
10. sin M = _____  _____
sin X = _____  _____
M
Z
Y
20
11.
tan L = _____  _____
tan Z = _____  _____
30
12. cos L = _____ _____
cos Z = _____  _____
K
16
X
16
L
13 - 24: Use a calculator to find the value correct to three decimal places.
13. sin 52  _____
14. cos 8  _____
15. tan 72  _____
16. sin 8  _____
17. cos 58  _____
18. tan 34  _____
19. sin 62  _____
20. cos 25  _____
21. tan 8  _____
22. sin 89  _____
23. cos 1  _____
24. tan 45  _____
25 – 12: Use a scientific calculator and/or trigonometric tables to find the lengths of the labeled sides. Write the
appropriate proportion, then solve. Round answers to 2 decimal places.
25. a = _____ b = _____
a
42
26. p = _____ q = _____
b
p
25
5
27. u = _____ v = _____
D
2
2
v
E
F
u
29. c = _____ d = _____
q
28. a = _____ b = _____
D
80
3
b
72
E
F
a
30. e = _____ f = _____
10
f
c
d
25
40
8
e
31. g = _____ h = _____
32. i = _____ j = _____
5
g
20
i
j
12
20
h
33. k = _____ l = _____
k
15
34. m = _____ n = _____
10
l
62
m
n
8
35. p = _____ q = _____
p
30
q
36. r = _____ s = _____
7
60
s
r
19
37. t = _____ u = _____
u
t
38. v = _____ w = _____
45
27
v
15
w
35
39. x = _____ y = _____
40. b = _____ c = _____
x
80
28
y
b
8
c
36
41 – 45: Write the appropriate proportion, then solve. Round answers to 2 decimal places.
X
41. To measure the width, XY, of a river, a surveyor walks along the bank
from point Y to point Z. She determines that mZ = 40 and ZY = 220 ft.
XY = _____
Z
42. A ramp designed for performing tricks on water skis has an angle of
elevation of 20. If the length of the ramp is 11 feet, what is the length
of the vertical drop (distance form the end of the ramp to the water)?
Y
11 ft
x
20
x = _____
5
x
43. A survey crew is planning a railroad line which rises to 1200
feet at a grade of 5. Solve for x, the length of the railroad line.
x = _____
44. A train is traveling up a slight grade with an angle
of inclination of only 2. After traveling 1 mile,
what is the vertical change in feet?
x = _____
45. A kite was flying 100 ft above the ground. The string was being
held at a 30 angle with ground. How long was the string?
_____
1 mile
2
1200 ft