Question

Prove that the height of the tower is h tan A / tan B - tan A

Answer 1

Answer:

height of Tower = hTanα/(Tanβ - Tanα)

Step-by-step explanation:

As we know that Tanθ  = Perpendicular Base

Let say Height of Tower = X

Bottom of Flag is top of tower

=> height of bottom of Flag = x

Let say point is d away from bootom of twoer

then Tanα = X/d  => d = X/Tanα

Top of Flag = Height Of Tower + Height of Flag = X + h

Tanβ  = (X + h)/d  => d = (X + h)/Tanβ

Equating d

=> X/Tanα = (X + h)/Tanβ

=> XTanβ = XTanα + hTanα

=>X(Tanβ - Tanα) = hTanα

=> X = hTanα/(Tanβ - Tanα)

Hence height of Tower = hTanα/(Tanβ - Tanα)