Question

two poles of height a meter and b meter are p meter apart . prove that height of point of intersection of the lines joining the top of each pole to the foot of opposite pole is given by ab/a+b

Answer 1

Solution:-Let the hight of the two poles be 'a' and 'b' meters respectively and let they be 'p' meters apart.Height of the pole AB = a meterHeight of the pole CD = b meterDistance between the poles = p metersLet the point of intersection of lines joining the top of the poles be 'E' and its height be 'h' meters. Suppose BF = x meter.Draw EF ⊥ BCIn Δ ABC and Δ EFC,∠ ACB = ∠ ECF      (Common)∠ ABC = ∠ EFC      (90°)∴ Δ ABC ~ Δ EFC   (AA similarity)⇒ AB/EF = AC/EC = BC/FC  (Corresponding sides are proportional)⇒ a/h = p/(p - x)⇒ ap - ax = ph  .....(1)Similarly,  Δ DCB ~ Δ EFB⇒ b/h = p/x⇒ x = ph/b  ......(2)From (1) and (2), we getap - aph/b = ph⇒ h(1 + a/b) = a⇒ h{(a + b)/b} = a⇒ h = ab/(a + b)Or, h = pq/(p + q)Hence proved.

Answer 2

Answer:

This is the answer