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, \(\theta = 39^{\circ}\), adjacent side is \(x\), and hypotenuse is \(16\). So, \(\cos(39^{\circ})=\frac{x}{16}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\cos(39^{\circ})=\frac{x}{16}\) by \(16\). We get \(x = 16\times\cos(39^{\circ})\).
Using a calculator, \(\cos(39^{\circ})\approx0.7771\). Then \(x=16\times0.7771 = 12.4336\).

Answer:

\(12.4\)