Question

7.) a man is in a boat that is floating 175 feet from the base of a 200 - foot cliff. what is the angle of depression between the cliff and the boat?

Explanation:

Step1: Identify right - triangle sides

We have a right - triangle where the height of the cliff is the opposite side ($a = 200$ feet) and the distance from the base of the cliff to the boat is the adjacent side ($b=175$ feet) 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, $\tan\theta=\frac{200}{175}=\frac{8}{7}$.

Step3: Find the angle

To find the angle $\theta$, we take the inverse tangent (arctan) of $\frac{8}{7}$. $\theta=\arctan(\frac{8}{7})\approx48.81^{\circ}$.

Answer:

Approximately $48.81^{\circ}$