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Need help solving thisIt’s a practice from my ACT prep guide online

Need help solving thisIt’s a practice from my ACT prep guide online-example-1
User Lxndr
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1 Answer

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If angles C and D are the acute angles of a right triangle, we have the image as shown below:

The question gives that:


\sin D=(2)/(7)

Comparing with the Sine Trigonometric Ratio given to be:


\sin \theta=(opp)/(hyp)

we thus have that the Sine ratio of angle D in the triangle drawn above will be:


\sin D=(d)/(b)

Hence, we can have the triangle look as shown below:

Therefore, the cosine of angle C, with the ratio:


\cos C=(adj)/(hyp)

will be given to be:


\cos C=(2)/(7)

Therefore, the correct option is the FIRST OPTION.

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