Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle LMN\) with right - angle at \(M\), for angle \(x\), the adjacent side is \(MN = 62\) and the hypotenuse is \(LN=90\). We use the cosine ratio: \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\).
So, \(\cos x=\frac{62}{90}\).

Step2: Solve for \(x\)

Take the inverse cosine of both sides: \(x = \cos^{-1}(\frac{62}{90})\).
Calculate \(\frac{62}{90}\approx0.6889\).
Then \(x=\cos^{-1}(0.6889)\).
Using a calculator, \(x\approx46.5^{\circ}\).

Answer:

\(46.5\)