Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the cosine of an angle \(x\) is defined as \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(x\) is \(KL = 47\) and the hypotenuse is \(LJ=73\). So, \(\cos x=\frac{47}{73}\).

Step2: Solve for \(x\)

Take the inverse cosine (arccos) of both sides. \(x = \cos^{-1}(\frac{47}{73})\).
Using a calculator, \(\frac{47}{73}\approx0.6438\). Then \(x=\cos^{-1}(0.6438)\approx50.0^{\circ}\)

Answer:

\(50.0\)