Question

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

Explanation:

Step1: Recall the sine function

In a right - triangle, the sine of an angle is defined as $\sin x=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, for angle $x$, the opposite side is $65$ and the hypotenuse is $75$. So, $\sin x=\frac{65}{75}$.

Step2: Calculate the value of $x$

We have $x = \sin^{-1}(\frac{65}{75})$. First, calculate $\frac{65}{75}=\frac{13}{15}\approx0.8667$. Then, $x=\sin^{-1}(0.8667)$. Using a calculator, $x\approx60.1^{\circ}$.

Answer:

$60.1^{\circ}$