A flagpole stands on top of a building. From a point 50 meters away from the base of the building, the angle of elevation to the top of the building is 30°, and to the top of the flagpole is 45°. Find the height of the flagpole.

Solution

Let the height of the building be h meters, and the height of the flagpole be f meters. From the angle of elevation to the top of the building (30°): tan 30° = h / 50 1/√3 = h / 50  h = 50 / √3. From the angle of elevation to the top of the flagpole (45°): tan 45° = (h + f) / 50   1 = (h + f) / 50   h + f = 50. Substitute h = 50 / √3: (50 / √3) + f = 50. f = 50 - (50 / √3). f = 50(1 - 1/√3). f = 50(√3 - 1) / √3. Answer: d