Question

the first step on a construction site is to have crews move the dirt so that the ground matches the drawings. the triangle matches the dimensions in the specifications. what is the measure of the angle of depression from the foundation to the sidewalk?

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the opposite side to the angle of depression (let's call the angle $\theta$) is 6 inches and the adjacent side is 16 inches. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan\theta=\frac{6}{16}=\frac{3}{8}$

Step2: Find the angle

To find the angle $\theta$, we take the inverse tangent (arctan) of $\frac{3}{8}$.
$\theta = \arctan(\frac{3}{8})$
Using a calculator, $\theta=\arctan(0.375)\approx20.56^{\circ}$

Answer:

$20.56^{\circ}$