Question

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

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( YZT \), \( \angle Z = 58^\circ \), opposite side to \( \angle Z \) is \( YT = 6.7 \), adjacent side is \( YZ = x \). Use tangent: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \), so \( \tan(58^\circ)=\frac{YT}{YZ}=\frac{6.7}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{6.7}{\tan(58^\circ)} \). Calculate \( \tan(58^\circ)\approx1.6003 \), then \( x=\frac{6.7}{1.6003}\approx4.2 \).

Answer:

\( 4.2 \)