Question

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

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( TUS \), \( \angle T = 90^\circ \), \( TU = 75 \), \( \angle S = 26^\circ \), and \( x \) is the hypotenuse. We use the sine function: \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). Here, \( \sin(26^\circ)=\frac{TU}{x} \), so \( \sin(26^\circ)=\frac{75}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{75}{\sin(26^\circ)} \). Calculate \( \sin(26^\circ)\approx0.4384 \). Then \( x=\frac{75}{0.4384}\approx171.1 \).

Answer:

\( 171.1 \)