Question

solve for x. round to the nearest tenth, if necessary. k 21 56° x j

Explanation:

Step1: Use the tangent function

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

Step2: Solve for \(x\)

Rearrange the equation to get \(x=\frac{21}{\tan(56^{\circ})}\). We know that \(\tan(56^{\circ})\approx1.4826\). Then \(x=\frac{21}{1.4826}\).

Step3: Calculate the value of \(x\)

\(x=\frac{21}{1.4826}\approx14.2\)

Answer:

\(14.2\)