Question

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 ?

Answer 1

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