Question

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

(image of a right triangle ijk with right angle at j, angle at i is 56 degrees, side jk is 21, side ij is x)

answer attempt 1 out of 2
x = input box submit answer

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(IJK\), \(\angle I = 56^\circ\), opposite side to \(\angle I\) is \(KJ = 21\), adjacent side is \(IJ = x\). We use tangent: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\), so \(\tan(56^\circ)=\frac{21}{x}\).

Step2: Solve for \(x\)

Rearrange the formula: \(x=\frac{21}{\tan(56^\circ)}\). Calculate \(\tan(56^\circ)\approx1.4826\), then \(x = \frac{21}{1.4826}\approx14.16\). Round to nearest tenth: \(x\approx14.2\).

Answer:

\(14.2\)