Question

solve for x in the triangle. round your answer to the nearest tenth. triangle image: right triangle, one leg is 13, angle 62°, other leg is x

Explanation:

Step1: Identify trigonometric ratio

In the right triangle, we have the side opposite the \(62^\circ\) angle as \(13\) and the adjacent side as \(x\). So we use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\).
\(\tan(62^\circ)=\frac{13}{x}\)

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{13}{\tan(62^\circ)}\)
Calculate \(\tan(62^\circ)\approx1.8807\)
Then \(x=\frac{13}{1.8807}\approx6.9\)

Answer:

\(6.9\)