Question

express sin w as a fraction in simplest terms.

Explanation:

Step1: Recall sine - ratio definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle W$, the side opposite to $\angle W$ is $YX = 18$, and we first need to find the hypotenuse $YW$.

Step2: Use the Pythagorean theorem

In right - triangle $YXW$, by the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 18$, $b = 24$, and $c$ is the hypotenuse $YW$. So $YW=\sqrt{18^{2}+24^{2}}=\sqrt{324 + 576}=\sqrt{900}=30$.

Step3: Calculate $\sin W$

$\sin W=\frac{YX}{YW}=\frac{18}{30}=\frac{3}{5}$.

Answer:

$\frac{3}{5}$