Question

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

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 26^{\circ}\), adjacent side is \(x\), and hypotenuse is \(47\). So, \(\cos(26^{\circ})=\frac{x}{47}\).

Step2: Solve for \(x\)

Multiply both sides by \(47\): \(x = 47\times\cos(26^{\circ})\). Using a calculator, \(\cos(26^{\circ})\approx0.8988\). Then \(x = 47\times0.8988 = 42.2436\approx42.2\).

Answer:

\(42.2\)