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 \(6.5\) and the hypotenuse is \(9.1\). So, \(\cos x=\frac{6.5}{9.1}\).

Step2: Calculate the value of \(x\)

First, simplify \(\frac{6.5}{9.1}=\frac{65}{91}=\frac{5}{7}\approx0.7143\). Then, use the inverse cosine function \(x = \cos^{-1}(0.7143)\). Using a calculator, \(x\approx44.4^{\circ}\).

Answer:

\(44.4\)