Solve for the height

Question

A flag pole is situated on top of a building. The angle of elevation from a point on level ground 330 feet from the building to the top of the flag pole is 63". The angle of elevation from the same point to the bottom of the flagpole is 53". Find the height of the flagpole to the nearest tenth of a foot.

Answer 1

There are two right triangles.

The smaller bottom one is made up of the ground which is one leg, the height of the building which is the other leg, and the distance from 330 feet away from the building to the bottom of the flagpole, which is the hypotenuse.

The angle between the ground and the hypotenuse is 53º.

tan=opposite/adjacent

x=height of the building

tan(53º)=x/330

tan(53º)(330)=x

(1.327)(330)=x

437.9 feet=x

The large triangle is made up of the ground, the height of the building and flagpole together, and the distance from 330 feet away from the building to the top of the flagpole. The angle is 63º.

tan(63º)=(437.9+y)/330 where y=height of the flagpole

1.9626=(437.9+y)/330

(1.9626)(330)=437.9+y

647.658=437.9+y

647.658-437.9=y

209.758=y

y=209.8 feet is the height of the flagpole