An electric pole is supported to stand vertically on a level ground by a tight wire. The wire is pegged at a distance of 6 meters from the foot of the pole. The angle that the wire makes the ground is three times the angle it makes with the pole.

Answer 1

We form a rt. triangle:
X = 6 meters = Hor.
Y = Ver. = Dist. from gnd to junction of wire and pole.
Z = Hyp. = Length of the wire.
A = Angle bet. gnd and wire.
B = Angle bet. pole and wire.

A + B = 90 Deg.
A = 3B.
3B + B = 90
B = 22.5 Deg.
A = 3B = 3*22.5 = 67.5 Deg.

Z*cosA = X
Z = X/cosA = 15.7 m.

tanA = Y/X = Y/6
Y = 6*tanA = 6*tan67.5 = 14.5 m.