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.