the angle of elevation of tower from a point A on ground is b, at B is 2b and at C is 3b.If AB =4BC/3, then prove sinb=5/12^1/2(5/12underoot)

Let height of tower be h and base of tower be called O. Also, let CO= y, BC=3x which implies AB= 4x.

Then tanb= h/(7x+y), tan2b= h/(3x+y) and tan3b= h/y. We also know that tan2b and tan3b are expressible in terms of tanb. Thus after elimination of all parameters but b, you shall obtain the equation:

12/7= 1+tan^2b= sec^2b

So sinb=√(1-7/12)

= √(5/12)