Question

What is the trigonometric ratio for sin Z ?

Answer 1

In all right triangles, the ratio between a leg and the hypothenuse is the sine of the angle opposite to the leg.

So, in your case, we have

$\sin(Z) = \dfrac{XY}{XZ}$

In order to find XY, we have

$XY = \sqrt{XZ^2-YZ^2} = \sqrt{1600-1024}=\sqrt{576} = 24$

So, the ratio for the sine is

$\sin(Z) = \dfrac{XY}{XZ} = \dfrac{24}{40} = \dfrac{3}{5}$