Question

This is the full question

Answer 1

Given: cos A = 5/13 = adj side / hypotenuse

The the opp side is given by (hypo)^2 = (adj)^2 + (opp)^2. Here,
13^2 = 5^2 + (opp)^2, so that
(opp)^2 = 169 - 25 - 144. Then opp = +12. All of these lengths are in Q I.
opp 12
Then sin A = -------- = -------- (answer)
hyp 13