Question

consider this right triangle. enter the length of side ac, to the nearest tenth.

Explanation:

Step1: Recall the tangent formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 57^{\circ}\), the opposite side to \(\theta\) is \(AC\), and the adjacent side is \(BC = 9\). So, \(\tan(57^{\circ})=\frac{AC}{9}\).

Step2: Solve for \(AC\)

We know that \(\tan(57^{\circ})\approx1.54\). Then \(AC = 9\times\tan(57^{\circ})\). Substitute \(\tan(57^{\circ})\approx1.54\) into the equation: \(AC\approx9\times1.54 = 13.86\approx13.9\).

Answer:

\(13.9\)