Question

a vertical tower substends a right angle at the top of a vertical flag on the ground ,the height of the flag being 10m . if the distance between the tower and the flag be 20m, find the height of the tower ​

Answer 1

Let AB be the flagstaff and CD be the vertical tower.

AB=10m=EC

BC=20m=AE

In triangle ABC we have,

tan x = AB/BC

tan x = 10/20

1/tan x = 20/10

10/tan x=20 --------------------- equation - 1

In triangle ADE we have

tan(90-x)=DE/AE

cot x=DE/20

1/cot x = 20/DE

DE/cot x = 20 ----------------------- equation - 2

By equation - 1 and equation 2 we get,

10/tan x  = DE/cot x

10/(AB/BC) = DE/(BC/AB)

10/(10/20) = DE/(20/10)

10×20/10 = DE×10/20

DE = 40m

Therefore height of vertical tower = DE+EC = 40+10 = 50m

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