Question

An ant looks up to the top of a building at an angle of elevation of 32°. Then, the ant walks an additional 88 feet from the edge of the building. If the new angle of elevation from the ant to the top of the building is 22°, find the height of the building. Round the answer to the nearest tenth.

Answer 1

tanα=h/x, tanß=h/(x+88)

solving both for x

x=h/tanα, x=h/tanß-88, since x=x

h/tanα=h/tanß-88

h/tanß-h/tanα=88

(htanα-htanß)/(tanα*tanß)=88

h(tanα-tanß)/(tanα*tanß)=88

h=88(tanα*tanß)/(tanα-tanß)

Since α=32 and ß=22...

h=88(tan32*tan22)/(tan32-tan22)

h≈85.3 feet