Question

solve for x. round to the nearest tenth of a degree, if necessary.
answer attempt 1 out of 2

Explanation:

Step1: Identify trigonometric ratio

Since we have a right - triangle with the opposite side to angle $x$ ($OH = 4.1$) and the hypotenuse ($OI=9.5$), 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, $\frac{4.1}{9.5}\approx0.4316$.
Then $x=\sin^{-1}(0.4316)$.
$x\approx25.6^{\circ}$.

Answer:

$x\approx25.6^{\circ}$