Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle \(x\) is given by \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(x\) is \(JK = 6.1\) and the hypotenuse is \(JL=8.8\). So, \(\cos x=\frac{6.1}{8.8}\).

Step2: Solve for \(x\)

Take the inverse cosine of both sides. \(x=\cos^{- 1}(\frac{6.1}{8.8})\).
Calculate \(\frac{6.1}{8.8}\approx0.69318\).
Then \(x = \cos^{-1}(0.69318)\).
Using a calculator, \(x\approx46.1^{\circ}\).

Answer:

\(46.1^{\circ}\)