Question

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

Explanation:

Step1: Recall the cosine function

In a right - triangle, \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(x\) is \(ST = 6.5\) and the hypotenuse is \(US=9.1\). So, \(\cos x=\frac{6.5}{9.1}\).

Step2: Calculate the value of \(x\)

First, compute \(\frac{6.5}{9.1}=\frac{65}{91}=\frac{5}{7}\approx0.714\). Then, use the inverse cosine function \(x = \cos^{-1}(0.714)\). Using a calculator, \(x\approx44.4^{\circ}\).

Answer:

\(x\approx44.4^{\circ}\)