On one side of a road of width ‘d’ meters there is a point of observation ‘p’ at a height ‘h’ meters from the ground. If a tree on the other side of the road, makes a right angle at ‘p’, height of the tree in meters is ?
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Answer:
T = (d² + h²)/h
Step-by-step explanation:
Angle of Depression from Point P at Bottom of tree
= α => angle of elevation from bottom of tree at point P = α
=> Tan α = Height of Point P /Distance of Road
=> Tanα = h/d
Angle of Elevation from P at top of Tree would be
90 - α (a tree on the other side of the road, makes a right angle at ‘p’)
Tan (90 - α) = Height of Tree Above p / Distnce of Road
=> Tan (90-α) = (T - h)/d ( T is height of Tree)
=> Cotα = (T - h)/d
=> Tanα = d/(T - h)
h/d = d/(T - h)
=> Th - h² = d²
=> Th = d² + h²
=> T = (d² + h²)/h
Height of Tree = (d² + h²)/h
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