Question

find the value of x. round to the nearest tenth.

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 32^{\circ}\), the adjacent side is \(x\), and the hypotenuse is \(40\). So, \(\cos(32^{\circ})=\frac{x}{40}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(32^{\circ})=\frac{x}{40}\) by \(40\). We get \(x = 40\times\cos(32^{\circ})\).
Since \(\cos(32^{\circ})\approx0.848\), then \(x = 40\times0.848 = 33.92\approx33.9\)

Answer:

\(33.9\)