In the equation below, the angle measures are in radians and a is a constant.

???(?/8)=???(?/?)

Which of the following could be the value of a ?

 

Useful fact to remember: if \angle A and \angle B are complementary (i.e., they add up to 90° or \dfrac{\pi}{2} radians), then \sin \angle A=\cos \angle B.

So I bet the question is getting at what a must be to make the angles add up to \dfrac{\pi}{2} ?

\dfrac{\pi}{8}+\dfrac{\pi}{a}=\dfrac{\pi}{2}\\\\ \dfrac{\pi}{8}+\dfrac{\pi}{a}=\dfrac{4\pi}{8}\\\\ \dfrac{\pi}{a}=\dfrac{3\pi}{8}\\\\ \dfrac{1}{a}=\dfrac{3}{8}\\\\ a=\dfrac{8}{3}

Of course, this question asks “which of the following” and there are actually an infinite number of answers, but that’s one of them.

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