Question

cos(arcsin(5/13))

Answer 1

Consider this trianlge having angle x there. Therefore, arcsin5/13 = x

Answer 2

Using pythagoren theorem we can solve for a. And a = 13^2 - 5^2 = 144 = 12
Hence cosx = 12/13 --> it also implies that cos(arcsin5/13) = 12/13 as well.

Answer 3

also, a = sqrt(13^2-5^2) = sqrt(144) = 12