Question

find the missing side.

13

32°

x = ?

round to the nearest tenth.
remember: sohcahtoa

Explanation:

Step1: Recall the sine formula

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 32^{\circ}$, the hypotenuse is $13$, and the opposite side is $x$. So, $\sin(32^{\circ})=\frac{x}{13}$.

Step2: Solve for $x$

Multiply both sides of the equation by $13$: $x = 13\times\sin(32^{\circ})$.
We know that $\sin(32^{\circ})\approx0.5299$. Then $x=13\times0.5299 = 6.8887$.

Answer:

$6.9$