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, the cosine of an angle \(x\) is defined as \(\cos x=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, the adjacent side to angle \(x\) is \(PQ = 7.2\) and the hypotenuse is \(QO=12\). So, \(\cos x=\frac{7.2}{12}\).

Step2: Calculate the value of \(\cos x\)

\(\frac{7.2}{12}=0.6\).

Step3: Find the angle \(x\)

We know that \(x = \cos^{-1}(0.6)\). Using a calculator, \(x\approx53.1^{\circ}\) (since \(\cos^{-1}(0.6)\approx53.13^{\circ}\) and rounding to the nearest tenth of a degree).

Answer:

\(x = 53.1\)