Question

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

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 56^{\circ}\), the opposite side to \(\theta\) is \(KJ = 21\), and the adjacent side is \(IJ=x\). So, \(\tan(56^{\circ})=\frac{KJ}{IJ}\).

Step2: Solve for \(x\)

Since \(\tan(56^{\circ})=\frac{21}{x}\), then \(x=\frac{21}{\tan(56^{\circ})}\). We know that \(\tan(56^{\circ})\approx1.4826\). So, \(x=\frac{21}{1.4826}\approx14.2\).

Answer:

\(14.2\)