the angle of elevation of the top of the tower from a point A on the ground is theta. on walking 85m towards the tower, the angle of elevation is found to be 2theta. if 2tantheta=8/15, calculate the height of the tower and the distance of tower from A.
refer to the diagram
please answer
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Answers
Height of the tower = 40 m , the distance of tower from A = 160 m
Step-by-step explanation:
Tan2θ = 8/15
Tan 2θ = 2Tanθ/(1 - Tan²θ)
=> 8/15 = 2Tanθ/(1 - Tan²θ)
=> 4 - 4Tan²θ = 15Tanθ
=> 4Tan²θ + 15Tanθ - 4 = 0
=> 4Tan²θ + 16Tanθ - Tanθ - 4 = 0
=> 4Tanθ(Tanθ + 4) - 1(Tanθ + 4) = 0
=> Tanθ = 1/4
Tan2θ = h/x => 8/15 = h/x => h = 8x/15
Tanθ = h/(x + 85) => 1/4 = h/(x + 85) => h = (x + 85)/4
8x/15 = (x + 85)/4
=> 32x = 15x + 15*85
=> 17x = 15 * 85
=> x = 15 * 5
=> x = 75
x + 85 = 75 + 85 = 160 m
h = 8x/15 = 8 * 75/15 = 40
Height of the tower = 40 m
the distance of tower from A = 160 m
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