Question

using trig to find a side
question
solve for x. round to the nearest tenth, if necessary.
answer
attempt 1 out of 3
x = submit answer

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \( \triangle IJK\), we know the adjacent side (\(IJ = x\)) to the angle \( \angle I=56^{\circ}\) and the opposite side (\(JK = 21\)). The trigonometric ratio that relates the opposite side and the adjacent side is the tangent ratio. The formula for tangent is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).

So, \(\tan(56^{\circ})=\frac{JK}{IJ}\).

Step2: Substitute the known values and solve for \(x\)

Substitute \(JK = 21\) and \(IJ=x\) into the tangent formula: \(\tan(56^{\circ})=\frac{21}{x}\).

We can rewrite this equation as \(x=\frac{21}{\tan(56^{\circ})}\).

We know that \(\tan(56^{\circ})\approx1.4826\).

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

Answer:

\(x = 14.2\)