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Question:If cos x = 5/7 and tan x = 4/5, what is sin x? A. 4/7 B. 7/9 C. 5/4 D. 9/7 E. 7/5 Answer:The correct answer is A.
The cosine of any acute angle is the length of the adjacent side divided by the hypotenuse (adj/hyp). The tangent of any acute angle is the length of the opposite side divided by the length of the adjacent side (opp/adj.) The sine of any acute angle is the length of the opposite side divided by the hypotenuse. You are given that cos x = 5/7 [adj/hyp] and tan x = 4/5 [opp/adj]. Sin x therefore must equal 4/7 [opp/hyp].
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