Question

express sin w as a fraction in simplest terms.
answer
attempt 1 out of 3
sin w =

Explanation:

Step1: Find the hypotenuse using Pythagorean theorem

$$\begin{align*} WY^2&=YX^2 + XW^2\\ WY^2&=18^2 + 24^2\\ WY^2&=324+576\\ WY^2&=900\\ WY& = 30 \end{align*}$$

Step2: Use the sine formula

The formula for sine in a right - triangle is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle W$, the opposite side to $\angle W$ is $YX = 18$ and the hypotenuse is $WY=30$.
So, $\sin W=\frac{YX}{WY}=\frac{18}{30}$

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor. The GCD of 18 and 30 is 6.
$\frac{18\div6}{30\div6}=\frac{3}{5}$

Answer:

$\frac{3}{5}$