Question

A ramp into a building forms a 6° angle with the ground. If the ramp is 8 feet long, how far away from the building is the entry point of the ramp? Round the solution to the nearest hundredth.

5.33 feet
6.05 feet
7.04 feet
7.96 feet

Answer 1

The distance from the building to the entry point of the ramp is approximately 7.96 feet, calculated using the cosine of a 6° angle and the length of the ramp as the hypotenuse (8 feet).

Step-by-step explanation:

To find the distance from the building to the entry point of the ramp, which is 8 feet long and forms a 6° angle with the ground, we can use trigonometry. Specifically, we are looking for the length of the adjacent side in a right-angled triangle, where the ramp serves as the hypotenuse, and the angle between the ramp and the ground is 6°.

The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse. Therefore:

cos(6°) = adjacent/hypotenuse

cos(6°) = distance from the building (entry point) / 8 feet

To solve for the distance from the building, we multiply both sides by the hypotenuse (8 feet):

distance from the building = 8 feet * cos(6°)

Using a calculator, we find that:

distance from the building = 8 feet * 0.9945

distance from the building ≈ 7.96 feet, when rounded to the nearest hundredth.

Therefore, the entry point of the ramp is approximately 7.96 feet away from the building.