Question

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

x =

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 44^{\circ}\), the adjacent side \(a = 6\), and the opposite side \(o=x\). So, \(\tan(44^{\circ})=\frac{x}{6}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\tan(44^{\circ})=\frac{x}{6}\) by \(6\). We get \(x = 6\times\tan(44^{\circ})\).
Since \(\tan(44^{\circ})\approx0.9657\), then \(x=6\times0.9657 = 5.7942\).

Answer:

\(x\approx5.8\)