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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

1 Answer

1 vote

Final answer:

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.

User Sashi
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