Question

find the sine of $\angle w$.
write your answer in simplified, rationalized form. do not round.
$\sin (w) = $

Explanation:

Step1: Recall sine definition for right triangles

In a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$

Step2: Identify sides for $\angle W$

Opposite side to $\angle W$ is $XY = 6$, hypotenuse is $XW = \sqrt{74}$

Step3: Substitute into sine formula

$\sin(W) = \frac{6}{\sqrt{74}}$

Step4: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{74}$:
$\sin(W) = \frac{6\sqrt{74}}{\sqrt{74} \times \sqrt{74}} = \frac{6\sqrt{74}}{74} = \frac{3\sqrt{74}}{37}$

Answer:

$\frac{3\sqrt{74}}{37}$