A surveyor is standing 50 feet from the base of a building. The angle of elevation to the top of the building is 60 degrees. Approximately how tall is the building?
height/50 = tan 60°
height = 50tan60 = appr 86.6 ft
To determine the height of the building, we can use the tangent of the angle of elevation. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
In this case, the opposite side is the height of the building and the adjacent side is the distance from the surveyor to the building.
Using the tangent function, we can set up the following equation:
tan(60 degrees) = height / 50 feet
The tangent of 60 degrees is √3.
√3 = height / 50
To find the value of height, we can multiply both sides of the equation by 50:
√3 * 50 = height
Height ≈ 86.6 feet
Therefore, the approximate height of the building is 86.6 feet.
To find the approximate height of the building, you can use trigonometry. In this case, you need to use the tangent function.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this scenario, the opposite side is the height of the building, and the adjacent side is the distance from the surveyor to the base of the building.
The tangent of 60 degrees is represented as tan(60°). We can set up the following equation:
tan(60°) = height of the building / 50 feet
Now, we can solve for the height of the building:
Height of the building = tan(60°) * 50 feet
Using a calculator, we find that tan(60°) is approximately 1.732.
Height of the building ≈ 1.732 * 50 feet
Therefore, the approximate height of the building is approximately 86.6 feet.