please explain it

[nocturne egret]

W0IK

[jovial isle]

$\frac{\pi}{2}<\alpha<\pi$ means it's in the second quadrant. Since ctg represents adj/opp, we can label those side lengths accordingly on the right triangle (note that length has sign now). Then, we see the hypotenuse has length $13$ using the Pythagorean theorem. \ \ Since sin is opp/hyp, $\sin \alpha=\frac{5}{13} \implies 52 \sin \alpha=\boxed{20}$.