Question

A vertical tower subtends a right angle on the top of 10m high flagstaff. if the distance between them is 20m, then find the height of the tower

Answer 1

Let AB be the flag staff and CD be the vertical tower.
AB=10m=EC
BC=20m=AE
let angle EAC =x
then angle DAE=90-x
In triangle,ABC we have,
tanx= AB/BC
tanx=10/20
1/tanx=20/10
10/tanx=20.............................1
In triangle ADE we have,
tan(90-x)=DE/AE
cotx=DE/20
1/cotx=20/DE
DE/cotx=20...........................2
by eq1 and. eq2 we get,
10/tanx=DE/cotx
10/(AB/BC)=DE/(BC/AB)
10/(10/20)=DE/(20/10)
10×20/10=DE×10/20
DE=40m
Therefore height of the vertical tower=DE+EC=40+10=50m