Question

find the exact value of sin z in simplest radical form.
right triangle with right angle at y, zy = 9, yx = 12, zx = 15

Explanation:

Step1: Recall sine definition

For angle $Z$, $\sin Z = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides

Opposite to $Z$ is $XY=12$, hypotenuse $ZX=15$

Step3: Simplify the fraction

$\sin Z = \frac{12}{15} = \frac{4}{5}$

Answer:

$\frac{4}{5}$