Question

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

Explanation:

Step1: Identify trigonometric ratio

For angle $x^\circ$, the opposite side is $LK = 69$, and the hypotenuse is $MK = 92$. Use the sine ratio: $\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$
<Expression>
$\sin(x) = \frac{69}{92}$
</Expression>

Step2: Simplify the fraction

Reduce $\frac{69}{92}$ to simplest form.
<Expression>
$\frac{69}{92} = \frac{3}{4} = 0.75$
</Expression>

Step3: Solve for $x$

Take the inverse sine of 0.75 to find $x$.
<Expression>
$x = \sin^{-1}(0.75)$
</Expression>

Step4: Calculate and round

Compute the value and round to the nearest tenth.
<Expression>
$x \approx 48.6^\circ$
</Expression>

Answer:

$48.6^\circ$