What is the degree measure of x in this triangle? Round only your final answer to the nearest hundredth.

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A. .01

B. 33.49

C. .55

D. 40.01

1 Answer
TwOfSpades
May 26, 2017

B, 33.49

Explanation:

We know the side lengths of the opposite side and the hypotenuse, so we need a trigonometric function to relate the two.

#sin(theta) = "opposite"/"hypotenuse"# works well in this case.

Now all we need to do is plug in everything we know, #theta# is #x#, opposite is the opposite side length, or 32, and hypotenuse is the long triangle side, or 58.
So:

#sin(x) = 32/58# We will use an inverse trigonometric function to get the angle:
#arcsin(32/58) = x#

After this we need a calculator, after plugging it into mine I get the answer is about answer B, 33.49.

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