Question

a cable is connected to the top of a building that is 20 feet high. the cable is attached to the ground 35 ft. away from the building.
what is the angle of depression from the top of the building to the ground?
40.31°
29.74°
51.68°
60.26°

Explanation:

Step1: Identify right - triangle values

We have a right - triangle where the height of the building is the opposite side ($a = 20$) and the distance from the building to the cable attachment on the ground is the adjacent side ($b = 35$) with respect to the angle of depression.

Step2: Use tangent function

The tangent of an angle $\theta$ in a right - triangle is given by $\tan\theta=\frac{a}{b}$. So, $\tan\theta=\frac{20}{35}=\frac{4}{7}$.

Step3: Find the angle

We need to find $\theta=\arctan(\frac{4}{7})$. Using a calculator, $\theta=\arctan(\frac{4}{7})\approx29.74^{\circ}$.

Answer:

$29.74^{\circ}$