Question

a building is 50 ft high. at a distance away from the building, a person notices that the angle of elevation with the ground to the top of the building is 41 how far is the person form the base of the building

Answer 1

To determine the distance from the person to the base of a 50 ft high building with a 41-degree angle of elevation, we use the tangent function.

By solving the equation distance = 50 ft / tangent(41 degrees), we calculate that the person is approximately 57.51 feet away from the base of the building.

Step-by-step explanation:

Using trigonometry, we will use the tangent function, which relates an angle of a right triangle to the ratio of the opposite side (the height of the building) to the adjacent side (the distance from the person to the building).

We have tangent (angle) = opposite/adjacent, so tangent (41 degrees) = 50 ft / distance form the base.

To find the distance, we rearrange the equation:

distance from the base = 50 ft / tangent(41 degrees).

Using a calculator, we find that tangent(41 degrees) ≈ 0.8693.

So the distance from the base ≈ 50 ft / 0.8693

≈ 57.51 ft.

Therefore, the person is approximately 57.51 feet away from the base of the building.