Question

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

Explanation:

Step1: Use trigonometric ratio (tangent)

In a right - triangle \( \triangle STU\), \(\tan U=\frac{opposite}{adjacent}\). Here, \(U = 39^{\circ}\), the side opposite to \(U\) is \(x\) and the side adjacent to \(U\) is \(75\). So, \(\tan U=\frac{x}{75}\).

Step2: Solve for \(x\)

Since \(\tan U=\frac{x}{75}\) and \(U = 39^{\circ}\), we can rewrite the equation as \(x = 75\times\tan(39^{\circ})\).
We know that \(\tan(39^{\circ})\approx0.80078\). Then \(x=75\times0.80078 = 60.0585\approx60.1\)

Answer:

\(x\approx60.1\)