A vertical tower stands on a horizontal plane and is surmounted by a Flagstaff of height hm

 

1. A vertical tower stands on a horizontal plane and is surmounted by a Flagstaff of height hm

A) h tanα/(tanβ- tanα)
B) h tanα/(tanα- tanβ)
C) h tanβ/(tanα- tanβ)
D) h (tanβ- tanα)

ANSWER= (A) h tanα/(tanβ- tanα)
Explain:-

 

answer:

Let the heigth of the tower is H m.

Here m is meter.

And the height of flagstaff is h.

The angles of elevation of the of  the bottom and top of the flagstaff are alpha and bita.

From the figure :

AB=h              BC=H

DC=x

In triangle BCD,

tanα=BC/DC

        =H/x

x=H/tanα

In triangle ADC,

tanβ =AC/DC

        =h+H/x

By putting the value of x,

tanβ =h+H/H/tanα

tanβ =(h+H)*tanα/H

H*tanβ=h tanα+H tanα

H(tanβ- tanα)=h tanα

H=h tanα/(tanβ- tanα)