Question

a pole 5m high is fixed on top of a tower. the angle of elevation of the top of the pole observed from a point A on the ground is 60degree and the angle of depression of the pointA from the top of the tower is 45degree. find the height of the tower

Answer 1

Let the height of the tower be h
now in triangle ABC
tan45=BC/AB
1=BC/AB
AB=BC
AB=h------(1)
now in triangle ABD
tan60=BD/AB
\/3=(5+h)/h. -----(from1)
\/3h=5+h
h(\/3-1)=5
h=5/(\/3-1)

where \/3 means underroot of 3...
BC is the height of tower...
CD is the height of pole on tower...
and AB is the dist of pt. A from the base of the tower...