Question

Express sin JJ as a fraction in simplest terms.
H
I
J
30
16
34

Answer 1

In triangle H I J the side lengths 30, 16, 34 satisfy 30^2 + 16^2 = 900 + 256 = 1156 = 34^2, so it's a right triangle with hypotenuse 34. ∠H is the right angle, so for ∠J the opposite side is HI = 30 and the hypotenuse is 34. Thus

sin J = 30/34 = 15/17.