Question

From the point on the ground 500 ft from the base of a building, it is observed that the angle of elevation to the top of the building is 24 degrees and the angle of tlevation to top top of a flagpole atop the building is 27 degress. Find the height of the building and the length of the flagpole.

Answer 1

Answer:

• building: 222.61 ft
• flagpole: 32.15 ft

Step-by-step explanation:

The tangent function of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Here, the adjacent side is 500 ft, so we have ...

  tan(24°) = (building height)/(500 ft)

  building height = (500 ft)tan(24°) ≈ 222.61 ft

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Similarly, the height to the top of the flagpole is ...

  total height = (500 ft)tan(27°) ≈ 254.76 ft

The length of the flagpole is the difference of these heights:

  flagpole length = 254.76 ft -222.61 ft = 32.15 ft

The height of the building is 222.61 ft; the length of the flagpole is 32.15 ft.