Question

the angle of elevation of the top of a tower from point a and b are away from the base and in the same straight line when it are 60 degree and 30 degree. prove that height of tower √ab​

Answer 1

Answer:

Let the height of the tower be h. Then in one case

tan 60= h/a equation 1

and in another case

tan 30=h/b

tan (90-60)=h/b

cot 60=h/b equation 2

Multiply equation 1 and equation 2

tan 60×cot 60=(h/a)×(h/b)=h2/(ab)

since tan60×cot60=1

1=h2/ab

h^2=ab

h=√(ab)