Question

An 8-foot long ramp goes from the back of a truck to the ground. The end of the ramp connected to the truck is 3 feet off of the ground. What is the angle of elevation of the ramp to the nearest degree

Answer 1

Answer: 22 degrees

Step-by-step explanation:

The angle of elevation of the ramp can be found using trigonometry. Specifically, we can use the sine function because we have the opposite side (height of 3 feet) and the hypotenuse (ramp length of 8 feet).

Using the formula:
$\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]$
$\[ \sin(\theta) = \frac{3}{8} \]$
We find the angle $\( \theta \)$ by taking the arcsine (inverse sine) of $\( \frac{3}{8} \)$
Therefore, the angle of elevation of the ramp is therefore approximately 22.02 degrees. Rounded to the nearest degree, the angle is 22 degrees.