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 ratio

We know the opposite side ($6$ inches) and the hypotenuse ($16$ inches) of the right - triangle. We use the sine function $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
Let the angle of depression be $\theta$. Then $\sin\theta=\frac{6}{16}=\frac{3}{8}$.

Step2: Find the angle

We use the inverse - sine function $\theta = \sin^{-1}(\frac{3}{8})$.
Using a calculator, $\theta=\sin^{-1}(\frac{3}{8})\approx22.02^{\circ}$.

Answer:

$22.02^{\circ}$