CBSE Class 10 Answered

Let AB be the tower.C and D be the two points  4m and 9m away respectively from B.

Let AB=h

Given,

 if angle ACB=x

 then angle ADB=90-x

So,

tan x=AB/4...(i)

tan(90-x)=AB/9...(ii)

so ,

 tanx =AB/4..(iii)

 and

 cot x= AB/9....(iv)

multiplying (iii) and (iv)

we get,

AB*AB=36

So,

 AB=6

So the height of the tower is 6m.

Note that we have used the fact that

tanx*cotx=1

 and also that whichever angle is x  doesn't matter as long as you take the other angle as its complimentary angle