Question

A cat climbs onto a roof and looks down at you. You are standing 12 feet away from the house, and there is an 18-foot diagonal distance between you and the cat. What is the angle of depression in which the cat is looking down at you? Round to the nearest whole degree.
A. 48°
B. 40°
C. 34°
D. 50°

Answer 1

To find the angle of depression from the cat to you, we can use the right triangle formed by the height of the cat on the roof, the distance from the base of the house to you, and the diagonal distance from the cat to you.

Given:
- Distance from you to the house (adjacent side): \( 12 \) feet
- Diagonal distance (hypotenuse): \( 18 \) feet

We can use the cosine relation (since we know the adjacent and hypotenuse) to find the angle \( \theta \):

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{12}{18}
\]

Calculating that:

\[
\cos(\theta) = \frac{12}{18} = \frac{2}{3}
\]

Now, we use the inverse cosine to find \( \theta \):

\[
\theta = \cos^{-1}\left(\frac{2}{3}\right)
\]

Calculating \( \theta \):

\[
\theta \approx 48.19°
\]

Since we need the angle of depression, it is equal to this angle because depression is measured downwards from the horizontal line at the height of the cat.

Rounding \( 48.19° \) to the nearest whole degree gives \( 48° \).

Thus, the angle of depression at which the cat is looking down at you is:

**A. 48°**