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
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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
Hope this helps you.
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