Question

solve for x.
17 cm
9 cm
x = ?°
round to the nearest hundredth.

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 \(9\) cm and the hypotenuse is \(17\) cm. So, \(\cos x=\frac{9}{17}\).

Step2: Solve for \(x\)

To find \(x\), we use the inverse cosine function. \(x = \cos^{-1}(\frac{9}{17})\).
Using a calculator, \(\cos^{-1}(\frac{9}{17})\approx58.04^{\circ}\) (rounded to the nearest hundredth).

Answer:

\(58.04\)