Billy is standing 80 feet from the base of a building. The angle of elevation to the top of the building is 35 degrees. If the distance from Billy's eyes to the ground is five feet, how tall is the building?
Please someone help!
To find the height of the building, we can use the concept of trigonometry, specifically the tangent function.
First, let's draw a diagram to visualize the situation. Let's represent the height of the building as "h."
Given:
Distance from Billy to the base of the building (adjacent side) = 80 feet
Angle of elevation to the top of the building = 35 degrees
Distance from Billy's eyes to the ground (opposite side) = 5 feet
Now, we can use the tangent function to determine the height (h) of the building:
Tangent(angle) = opposite / adjacent
Tangent(35 degrees) = h / 80 feet
To find the value of the tangent of 35 degrees, we can use a scientific calculator.
Tan(35 degrees) ≈ 0.7002
Now, we can solve for the height of the building (h):
0.7002 = h / 80
h = 0.7002 * 80
h ≈ 56.016
Therefore, the approximate height of the building is 56.016 feet.