tanθ = 4.5/16
so, θ = ?
so, θ = ?
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.