Question

solve for x. round to the nearest tenth, if necessary. triangle with right angle at t, angle at u is 39 degrees, side tu is 75, side st is x

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( STU \), \( \angle U = 39^\circ \), \( TU = 75 \), \( ST = x \), and \( \angle T = 90^\circ \). We use the tangent function: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). Here, \( \tan(39^\circ)=\frac{ST}{TU}=\frac{x}{75} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = 75\times\tan(39^\circ) \). Calculate \( \tan(39^\circ)\approx0.8098 \), so \( x\approx75\times0.8098 = 60.735 \approx 60.7 \) (rounded to the nearest tenth).

Answer:

\( 60.7 \)