## 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

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].

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].