Asked by anonymous
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.
Answers
Answered by
Henry
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.
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.
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