A person is 600 feet away from a building that is 300 tall l

A person is 600 feet away from a building that is 300 tall, looking up at the top of the building. On top of the building is a big flagpole. If the person needs to look upward an additional angle of arctan(1/12) to look at the flag, how tall is the flagpole?

NB:No calculator allowed.

Solution

Base = B = 600 feet

height of building = H = 300 feet

Angle = arctan(H/B) = 26.6 degree

Now to look at the flag, angle = 26.6 + arctan(1/12) = 31.36 degree

Then height of flagpole = 600*tan31.36 - 300 = 65.7 feet