Trig Word Problem

Question

A person is standing 250 ft from the base of a tall building. The angle of elevation to the top of the building is 63 degrees. the angle of elevation to the top of the antenna located on the roof the building is 68 degrees. How tall is the antenna?

Answer 1

Use the following trig relationships. Let x = the height of the antenna and y the height of the building in relation to the person. So tan 63 = y/250 and tan 68 = (x+y)/ 250. So y= 250•tan63 and x = 250•tan68 - y and this gives x= 250( tan68 - tan63). Using a trig table x = 250( 2.475 -1.962) = 128.25 ft. This is the height of the antenna.

Answer 2

Construct a right triangle. One angle is 63 degree with adjacent side 250. The height of the building is the length of the opposite side which is 250tan63 = 490.65

Do the same for the antenna. To find how far antenna is above ground 250tan68 = 618.77

To find how tall the antenna is 618.77-490.65= 128.12