Question

find x. round your answer to the nearest tenth of a degree.

Explanation:

Step1: Identify the trigonometric ratio

We know the opposite side ($11$) and the hypotenuse ($20$) of the right - triangle with respect to angle $x$. We use the sine ratio $\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin(x)=\frac{11}{20}$.

Step2: Solve for $x$

To find $x$, we take the inverse - sine of both sides: $x = \sin^{-1}(\frac{11}{20})$.
Using a calculator, $\sin^{-1}(\frac{11}{20})\approx33.4^{\circ}$.

Answer:

$33.4$