Question

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

Explanation:

Step1: Find the measure of angle \( V \)

In right - triangle \( VUT \), the sum of angles is \( 180^{\circ} \). Since \( \angle U = 90^{\circ} \) and \( \angle T=70^{\circ} \), then \( \angle V=180^{\circ}-(90^{\circ} + 70^{\circ})=20^{\circ} \)

Step2: Use trigonometric ratio (tangent)

We know that \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). In \( \triangle VUT \), for \( \angle T = 70^{\circ} \), \( \tan(70^{\circ})=\frac{x}{64} \) (where \( x \) is the side opposite to \( \angle T \) and \( 64 \) is the adjacent side to \( \angle T \))

Step3: Solve for \( x \)

$$ x = 64\times\tan(70^{\circ}) $$

Since \( \tan(70^{\circ})\approx2.747 \), then \( x = 64\times2.747=175.808\approx175.8 \)

Answer:

\( x\approx175.8 \)