Question

A 40-foot television antenna stands on top of a building. From a point on the ground, the angles of elevation of the top and bottom of the antenna, respectively, have measurements of 56 degrees and 42 degrees. How tall is the building?

Answer 1

The building is (approximately) `62` feet tall.

Explanation:

`b/d = tan(42^@) = 0.900404`
`color(white)("XXX")rarr d = b/0.900404`

`(40+b)/d = tan(56^@) = 1.482561`
`color(white)("XXX")rarr 40+b = (b/0.900404)xx1.482561`

`color(white)("XXX")rarr b+40=1.646550766xxb`

`color(white)("XXX")rarr 0.64655076xxb = 40`

`color(white)("XXX")rarr b = 40/0.64655076 = 61.86675838`