Question

solve for x. round to the nearest tenth of a degree, if necessary.

Explanation:

Step1: Identify trigonometric ratio

We use sine ratio since $\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, opposite side to angle $x$ is $45$ and hypotenuse is $89$. So, $\sin(x)=\frac{45}{89}$.

Step2: Solve for $x$

We take the inverse - sine of both sides: $x = \sin^{-1}(\frac{45}{89})$.
Using a calculator, $x=\sin^{-1}(\frac{45}{89})\approx30.4^{\circ}$.

Answer:

$30.4^{\circ}$