Question

solve for (x). round to the nearest tenth of a degree, if necessary. answer attempt 1 out of 2 (x=)

Explanation:

Step1: Identify trigonometric ratio

In right - triangle LMN, we know the opposite side (5.5) and the adjacent side (4.2) to angle \(x\). We use the tangent function \(\tan(x)=\frac{\text{opposite}}{\text{adjacent}}\). So \(\tan(x)=\frac{5.5}{4.2}\).

Step2: Solve for \(x\)

We take the inverse - tangent of both sides. \(x = \tan^{- 1}(\frac{5.5}{4.2})\).
Using a calculator, \(\frac{5.5}{4.2}\approx1.3095\), and \(x=\tan^{-1}(1.3095)\approx52.6^{\circ}\).

Answer:

\(x\approx52.6\)