Question

solve for ( x ). round to the nearest tenth, if necessary.
(there is a right triangle ( uvt ) with right angle at ( u ), ( ut = 64 ), ( angle t = 70^circ ), and ( uv = x ))
answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( UTV \), \( \angle T = 70^\circ \), \( UT = 64 \) (adjacent side to \( \angle T \)), and \( x = UV \) (opposite side to \( \angle T \)). We use the tangent function: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). So, \( \tan(70^\circ)=\frac{x}{64} \).

Step2: Solve for \( x \)

Multiply both sides by 64: \( x = 64\times\tan(70^\circ) \). Calculate \( \tan(70^\circ)\approx2.7475 \), then \( x = 64\times2.7475\approx175.8 \).

Answer:

\( x \approx 175.8 \)