Answer: The flagpole is 75.6 feet (approximately)
Step-by-step explanation: Please refer to the picture attached.
The man is at point C and the base of the building is point B, and he looks up at an angle of elevation of 60 degrees to the bottom of the flagpole. Note that the flagpole is attached to the top of the edge of the building which is point A. Also he looks up at an angle of elevation of 62.5 degrees to the top of the flagpole which is point A.
If his distance from the base of the building is 400 feet (line BC), then we would start by calculating the height of the building plus the flagpole (line FB) and then the height of the building itself (line AB) and the difference between both would be the height of the flagpole (line FA).
We shall use the trigonometric ratios as follows;
In triangle FBC,
Tan C = opposite/adjacent
Tan 62.5 = FB/400
Tan 62.5 x 400 = FB
1.9209 x 400 = FB
768.36 = FB
Also in triangle ABC,
Tan C = opposite/adjacent
Tan 60 = AB/400
Tan 60 x 400 = AB
1.732 x 400 = AB
692.8 = AB
The height of the vertical flagpole can be derived as
FA = FB - AB
FA = 768.36 - 692.8
FA = 75.56
FA ≈ 75.6
Therefore the height of the flagpole is 75.6 feet (approximately)
