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 $7.4$, hypotenuse is $13$. Use sine: $\sin(x) = \frac{\text{opposite}}{\text{hypotenuse}}$
<Expression>$\sin(x) = \frac{7.4}{13}$</Expression>

Step2: Calculate ratio value

Compute the decimal value of the fraction.
<Expression>$\frac{7.4}{13} \approx 0.5692$</Expression>

Step3: Find inverse sine

Use $\arcsin$ to solve for $x$.
<Expression>$x = \arcsin(0.5692)$</Expression>

Step4: Compute and round result

Calculate the angle and round to nearest tenth.
<Expression>$x \approx 34.7^\circ$</Expression>

Answer:

$34.7^\circ$