Question

A 350-foot water slide has a 32-foot vertical drop. What is the angle of depression?

Answer 1

Please find the attached diagram for a better understanding of the solution given here.

B is the base of the Vertical Drop. Thus, AB=32 feet.

AC is the water slide and thus the length of AC is 350 feet.

We need to find the angle of depression which in this case is $\angle X$.

As can be seen from the diagram, $\angle Y$ and $\angle X$ are alternate interior angles where the water slide, AC, is the transversal and thus they will be equal.

therefore, $\angle X = \angle Y$

Let us make use of the $\Delta ABC$ to find $\angle Y$ using the Sine trigonometric ratio.

Thus, $Sin (\angle Y)=\frac{Opposite Side}{Hypotenuse} =\frac{AB}{AC}$

$\therefore Sin(\angle Y)=\frac{32}{350}$

$\angle Y=Sin^{-1}(\frac{32}{350})=\approx5.246^0$

Thus Angle of Depression is $5.246^0$, which the required answer.