Since you are looking for the distance between the base of the ladder and the wall,
represented by x, you are dealing with the side that is adjacent to the 65° angle as well as the
hypotenuse. Since cosine is defined as , cos 65 = . Multiply both sides by 10
to get x = 10 cos 65, which is (C).
29 . D Because quadrilateral GHJK has four right angles, it is a rectangle, and GK measures 30
inches. We must use SOHCAHTOA to determine the side lengths of right triangle FGK,
eliminating (A) and (B). Since we know the measure of F, use SOH: sin 70° = , which
rearranges to give FK = .
35 . A We know the side adjacent to angle θ and the hypotenuse, so use CAH to set up the problem:
cosθ = . To determine the measure of angle θ, use the inverse function cos−1,
eliminating (B), (C), and (E). Choice (D) incorrectly uses the reciprocal of .
37 . D Remember SOHCAHTOA! We’re given the side opposite the 65° angle, and we want to find
the hypotenuse, so we need the sine function. Plug the information you have into the function:
sin 65° = (where x is the length of the ladder). Multiply both sides by x to get x sin 65° =
12. Then divide by sin 65° to get x = . The correct answer is (D).
