posted by Dd .
two poles 6m and 15m tall are 20 m apart a wire is attached to the top of each pole and is also staked to the ground some where b/n two poles where should be the wire be staked so that the minimum amount of wire be used?
make a sketch.
draw poles AB and PQ with B and Q on the ground
Draw the reflection of AB in the horizontal and call it BA'. Joint A' to P
Label the intersection of A'P with BQ as M.
let BM = x, then
MQ = 20-x
Of course the shortest distance between any two points is the straight line joining them, So A'P is the shortest
but A'P = AM + MP <--- the shortest
since triangles ABM and PQM are similar,
AB/BM = PQ/MQ
6/x = 15/(20-x)
15x = 120 - 6x
21x = 120
x = 120/21 = 40/7
Attach it 40/7 m from B