Help with geometry question, height of building?

[Grizzllyy]

A surveyor measures the angle of elevation of the top of a building to be 60 degrees. The surveyor then walks 100 feet farther from the base of the tower and measures the angle of elevation to be45 degrees. The surveyor's angle-measuring device is 5 feet from the ground. How tall is the building to the nearest foot?

 

[tkhunny]

Please draw two right traingles.

1a) Building less the first 5 feet is the vertical leg. Right angle at the bottom.
1b) Acute angle at surveyor = 60º
1c) Distance to building (horizontal leg) is "D".

2a) Building less the first 5 feet is the vertical leg. Right angle at the bottom.
2b) Acute angle at surveyor = 45º
2c) Distance to building (horizontal leg) is "D+100".

Let's see what you get.

RBGTHGANH

 

[Deleted member 4993]

A surveyor measures the angle of elevation of the top of a building to be 60 degrees. The surveyor then walks 100 feet farther from the base of the tower and measures the angle of elevation to be45 degrees. The surveyor's angle-measuring device is 5 feet from the ground. How tall is the building to the nearest foot?

First draw a sketch of the situation.

Assume that

you are "x" ft away from the building - and

the height of the building = h ft

then

tan(60°) = (h-5)/x

then

tan (45°) = (h-5)/(x+100)

Now solve for "h" from above.