Question

what is the angle of depression from the start of a 6 - foot - high access ramp that ends at a point 40 feet away along the ground?
a. 0.15°
b. 8.2°
c. 8.5°
d. 45.6°

Explanation:

Step1: Use the tangent function

The tangent of the angle of depression $\theta$ in a right - triangle is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the height of the ramp (opposite side) $y = 6$ feet and the horizontal distance (adjacent side) $x=40$ feet. So, $\tan\theta=\frac{6}{40}=0.15$.

Step2: Find the angle

To find the angle $\theta$, we use the inverse tangent function. $\theta=\tan^{- 1}(0.15)$. Using a calculator, $\theta\approx8.5^{\circ}$.

Answer:

C. $8.5^{\circ}$