Trigonometry
24 . J Since you are asked to find the opposite side of a particular angle, and you are given the
hypotenuse, use the first part of SOHCAHTOA, which indicates that sin θ = .
Substitute the given information to find 78° = . Multiply each side of the equation by 9, so x
= 9. Using the provided approximation for 78°, x = 9 × 0.9781 = 8.8029, which rounds to
8.803. Choice (H) is close, but it isn’t the closest approximation. If you picked (K), you may
have found the tangent instead of the sine.
28 . F First, since the hypotenuse of the triangle must be its longest side, eliminate (H), (J), and (K).
Given that sinθ = , use SOHCAHTOA. This means that sinθ = , so you can
set up a proportion to find the length of the hypotenuse. Let x be the length of the hypotenuse,
and sinθ = . Set the two values for sin θ equal to each other to get . Solve the
equation by multiplying each side by 13x to 5x = 234, or x = 46.8 feet. If you picked (G), be
careful: This is the horizontal distance between Mario and the flagpole.
35 . C In the figure, you are given the hypotenuse of the right triangle, as well as the side that is
opposite the indicated angle θ. Therefore, use SOHCAHTOA, specifically the relationship of
sinθ = . Substitute the information given in the question to find sinθ = . To
solve for the value of θ, take the inverse sine of each side of the equation, which would give
sin−1(sinθ) = sin−1 . The inverse sine function and sine function cancel each other out,
leaving you with θ = sin−1.
48 . G Redraw the right triangle with a 33° angle and a hypotenuse of length 550 yards. The length
of the leg adjacent to the 33° angle is the distance due east, and the length of the leg opposite
the 33° angle is the distance due south. To figure out the lengths of those legs, choose one and
use SOHCAHTOA. To find the distance due south, or the distance opposite the given angle,
