Question

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

Explanation:

Step1: Identify trigonometric ratio

Since we have a right - triangle with opposite side to angle $x$ of length $4.1$ and hypotenuse of length $9.5$, we use the sine ratio $\sin x=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $\sin x=\frac{4.1}{9.5}$.

Step2: Solve for $x$

We know that $x = \sin^{- 1}(\frac{4.1}{9.5})$. Using a calculator, $\frac{4.1}{9.5}\approx0.4316$, and $x=\sin^{-1}(0.4316)$. Then $x\approx25.6^{\circ}$.

Answer:

$25.6^{\circ}$