Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( RQS \), \( \angle Q = 40^\circ \), \( RS = 35 \) (opposite to \( \angle Q \)), and \( x = SQ \) (hypotenuse). We use the sine function: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \). So \( \sin(40^\circ) = \frac{35}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{35}{\sin(40^\circ)} \). Calculate \( \sin(40^\circ) \approx 0.6428 \). Then \( x \approx \frac{35}{0.6428} \approx 54.5 \).

Answer:

\( 54.5 \)