Question

A flagpole 40 feet high stands on top of the a building. From a point in front of the store, the angle of elevation for the top of the pole is 54° 54', and the angle of elevation for the bottom of the pole is 47° 30'. How high is the building?

Answer 1

The building is `131.66` feet high (approximately)

Explanation:

If the horizontal distance to the building is `x` feet
and the building is `y` feet high
(and assuming the flag pole is at the near edge of the building):

`y/x = tan(47^@30')`
`color(white)("XXXXXXX")rarr x= y/tan(47^@30')`

`(y+40)/x = tan(54^@54')`
`color(white)("XXXXXXX")rarr x=(y+40)/tan(54^@54')`

`y/tan(47^@30') = (y+40)/tan(54^@54')`

Simplifying:
`y = (40*tan(47^@30'))/(tan(54^@30')-tan(47^@30'))`

Using a calculator to determine actual values of the `tan` terms and perform the calculation:
`color(white)("XXXX")y ~=131.66`