Question

solve for x in the triangle. round your answer to the nearest tenth.

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 42^{\circ}\), the hypotenuse is \(13\), and the adjacent side is \(x\). So, \(\cos(42^{\circ})=\frac{x}{13}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(42^{\circ})=\frac{x}{13}\) by \(13\). We get \(x = 13\times\cos(42^{\circ})\).
Using a calculator, \(\cos(42^{\circ})\approx0.7431\). Then \(x=13\times0.7431 = 9.6603\).

Answer:

\(9.7\)