Sadie the dog is sitting on the roof of his doghouse, 4.5 ft off the ground. He is watching a cat that is 16 ft away from the base of the doghouse. What is the angle of depression from the roof of the doghouse to the cat? Round to the nearest hundredth.

tanθ = 4.5/16

so, θ = ?

To find the angle of depression from the roof of the doghouse to the cat, we can use trigonometry. The angle of depression is the angle formed between a horizontal line (line of sight) from the observer (roof of the doghouse) and the line of sight to the object being observed (cat).

In this case, the height of the doghouse (4.5 ft) and the horizontal distance from the doghouse to the cat (16 ft) form a right triangle. To find the angle of depression, we can use the tangent ratio:

tangent(angle) = opposite/adjacent.

Here, the opposite side is the height of the doghouse (4.5 ft) and the adjacent side is the horizontal distance from the doghouse to the cat (16 ft).

Thus, we have:

tangent(angle) = 4.5/16.

To find the angle, we need to take the inverse tangent (also known as arctangent) of this ratio. In mathematical notation, we have:

angle = arctan(4.5/16).

Using a calculator or a computer, we can evaluate this expression:

angle ≈ 16.39 degrees.

Therefore, the angle of depression from the roof of the doghouse to the cat is approximately 16.39 degrees rounded to the nearest hundredth.