Question

solve for x in the triangle. round your answer to the nearest tenth.

Explanation:

Step1: Identify trigonometric relation

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 29^{\circ}$, the opposite - side to the angle is 11 and the hypotenuse is $x$. So, $\sin(29^{\circ})=\frac{11}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{11}{\sin(29^{\circ})}$. Since $\sin(29^{\circ})\approx0.4848$, then $x=\frac{11}{0.4848}\approx22.7$.

Answer:

$22.7$