Final answer:
Using the tangent function, the angle of elevation from the fire hydrant to the top of the 125-foot tall building, which is 72 feet away from the base, is approximately 60.255 degrees.
Step-by-step explanation:
To find the angle of elevation from the fire hydrant to the top of the building, we can use trigonometry, specifically the tangent function. In this scenario, we have a right triangle where the building forms one side (the opposite side to the angle of elevation), the distance from the fire hydrant to the building forms the adjacent side, and the diagonal line of sight from the fire hydrant to the top of the building forms the hypotenuse.
Let's call the angle of elevation θ (theta). The height of the building is 125 feet and the distance from the hydrant to the building is 72 feet. Using the tangent function, we have:
The formula to find θ is:
θ = tan⁻¹(opposite/adjacent)
θ = tan⁻¹(125 feet / 72 feet)
Calculating this using a calculator gives us:
θ ≈ tan⁻¹(1.7361)
θ ≈ 60.255 degrees
The angle of elevation from the fire hydrant to the top of the building is approximately 60.255 degrees.