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