Question

find the missing side.
z
21
31°
z = ?

Explanation:

Step1: Identify trigonometric ratio

In a right triangle, $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 31^\circ$, opposite side is 21, hypotenuse is $z$. So $\sin(31^\circ)=\frac{21}{z}$.

Step2: Solve for \( z \)

Rearrange the formula: $z=\frac{21}{\sin(31^\circ)}$. Calculate $\sin(31^\circ)\approx0.5150$. Then $z=\frac{21}{0.5150}\approx40.78$.

Answer:

\( z\approx40.8 \) (rounded to one decimal place, or more precise as needed)