Question

solve for x. round to the nearest tenth of a degree, if necessary.

Explanation:

Step1: Identify trigonometric ratio

In right - triangle LMN, we know the adjacent side to angle \(x\) (\(MN = 9.1\)) and the hypotenuse (\(LN=15\)). We use the cosine function, \(\cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(x)=\frac{9.1}{15}\).

Step2: Solve for \(x\)

We take the inverse - cosine of both sides: \(x = \cos^{-1}(\frac{9.1}{15})\). Calculate \(\frac{9.1}{15}\approx0.6067\). Then \(x=\cos^{-1}(0.6067)\). Using a calculator, \(x\approx52.6^{\circ}\).

Answer:

\(x\approx52.6\)