Question

Emily places a loading ramp next to her truck. The height of the ramp is 6

feet, and an inclined portion of the ramp is 22
feet long. What angle does the ramp make with the ground?



Round your answer to one decimal place.

Answer 1

The angle the ramp makes with the ground is approximately 15.9 degrees, determined using the sine function and the given dimensions of the ramp.

Step-by-step explanation:

To calculate the angle that the ramp makes with the ground, we can use trigonometry, specifically the sine function, which relates the opposite side to the hypotenuse in a right-angled triangle. The height of the ramp (6 feet) is the opposite side, and the length of the ramp (22 feet) is the hypotenuse.

The sine function is defined as:
sin(angle) = opposite/hypotenuse

Therefore, to find the angle, we take the inverse sine (also known as arcsin) of the height divided by the length of the ramp:

angle = arcsin(6 feet / 22 feet).

Performing this calculation:

angle = arcsin(0.2727) ≈ 15.9 degrees

Hence, the angle the ramp makes with the ground is approximately 15.9 degrees, rounded to one decimal place.