Question

An antenna is located at the top of a building 1000 ft tall. From a point on the same horizontal plane as the base of the building, the angles of elevation from the top and the bottom of the antenna are 65.8 degrees and 62.6 degrees respectively. How tall is the antenna.

Thanks

Answer 1

Make a sketch, I have 2 right-angled triangles
Let the point of observation be x ft from the building, let the height of the antenna be h ft
then
tan 62.2 =100/x
x = 100/tan62.2 = 52.724... (I stored in memory to keep accuracy)

In 2nd triangle
tan 65.8 = (h+100)/x
h+100 = xtan65.8
h = 52.724(tan65.8) - 100 = 17.32 ft