Question

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At distances of 18m and 2m the angles of elevation of a tower are complementary .Find the height of the tower.​

Answer 1

Height of tower = 6m if at distances of 18m and 2m the angles of elevation of a tower are complementary

Step-by-step explanation:

Let say height of tower = H

one angle of elevation = a

another angle of elevation = 90-a

as both angles are complementary

Tana = H /2

Tan (90-a) = H/18

Tan(90-a) = Cota

Cots = H/18

Tan a * Cota = (H/2)(H/18)

1 = H^2/36

H^2 = 36

H^2 = 6^2

H = 6

Height of tower = 6m

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Answer 2

Let

Height=h

One angle be x

Another be 90-x

If both are complementary than

Tan x= H/2

Tan(90-x)=H/18

Tan(90-x)=cot x

Acc to formula

Tan x×cot x= H/2×H/18

1=H^2/36

H=6m

Height of a tower = 6m