Question

teshale is standing on a cliff 15 meters above the ground. his line of sight forms a 56° angle of depression to an antelope on the ground in the distance. assuming the cliff forms a right angle with the ground, find the distance from the bottom of the cliff to the antelope. 8.39 meters 22.24 meters 10.12 meters 12.44 meters

Explanation:

Step1: Use the tangent function

Let \(d\) be the distance from the bottom of the cliff to the antelope. The angle of depression is \(56^{\circ}\), and the height of the cliff \(h = 15\) meters. The angle of depression is equal to the angle of elevation from the antelope to Teshale. So, \(\tan\theta=\frac{opposite}{adjacent}\), where \(\theta = 56^{\circ}\) and the opposite side is the height of the cliff (\(15\) meters) and the adjacent side is \(d\).
\(\tan(56^{\circ})=\frac{15}{d}\)

Step2: Solve for \(d\)

\(d=\frac{15}{\tan(56^{\circ})}\)
We know that \(\tan(56^{\circ})\approx1.4826\)
\(d=\frac{15}{1.4826}\approx10.12\)

Answer:

10.12 meters