Question

Two poles of height a and b metres are standing vertically on the ground p metre apart. Prove that the height of the point of intersection of the joining the top of each pole to the foot of opposite poleis given by ab/a+b metres.

Answer 1

Let the height of the two trees AB and CD be b and a respectively.
Distance between the trees BC = p
Let EF = h be the height of point of intersection of the lines joining the top of each tree to the foot of the opposite trees.
Let CF = x then BF = (p – x)
In Δ’s ABC� and EFC,
∠ABC = ∠EFC = 90°
∠C = ∠C (common angle)
∴ ΔABC ~ ΔEFC (By AA similarity theorem)

Similarly, ΔDCB ~ ΔEFB (By AA similarity theorem)
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