ACT Math: More Right Triangle Trigonometry (SOH-CAH-TOA) Problems

Whenever I look at the statistics for this blog, one of the most popular pages is always the post on Right Triangle Trigonometry (SOH-CAH-TOA) Problems. With that in mind, it made sense to create some more of this problems for you to try (give the people what they want, right?). So grab your calculator and a pencil and let’s give these a try!

1.  In the right triangle below, what is the value of tan A?


A.  5/12
B.  5/13
C.  12/13
D.  12/5
E.  13/5

2.  Sarah has pegged her kite to the ground and is watching it fly. When 150 feet of string are out, the kite is 82 feet above the level ground. What angle, to the nearest tenth of a degree, is the kite making with the ground?


F.  28.7
G.  33.1
H.  42.3
J.  47.5
K.  56.9

3.  The hypotenuse of right triangle JKL is 12 units long. If cos K is 3/4, what is the length, in units, of segment LK?


A.  8
B.  9
C.  10
D.  11
E.  16

4.  A ramp is 23 feet long and at its highest point it is 1.5 feet above the level ground.  What angle, to the nearest tenth of a degree, does the ramp make with the ground?

F.  3.2
G. 3.5
H.  3.7
J.  4.1
K.  4.4

5.  An angle θ has one side along the positive x-axis. One point on the terminal side of the angle is (-7, 24). What is the value of cos θ?


A.  -24/25
B.  -7/25
C.  -7/24
D.  7/25
E.  24/25

6.  For all values of θ, (3cosθ + 3sinθ)² is equivalent to which of the following?

F.  3cos²θ + 3sin²θ
G.  9cos²θ + 9sin²θ
H.  9cos²θ + 9cosθsinθ + 9sin²θ
J.  9 + 9cosθsinθ
K.  9 + 18cosθsinθ 

If you have questions about these problems or anything else to do with the ACT, leave a comment below or send me an email at


1.  A
2.  G
3.  B
4.  H
5.  B
6.  K

(Note: If you need to review more advanced trigonometry problems like #5 and #6, take a few minutes to read this post.)

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