An electric pole is 10 m high. A steel wire tied to the top of the pole isaffixed at a point on the ground to keep the pole upright. If the wiremakes an angle of 45º with the horizontal through the foot of the pole,find the length of the wire.
Given:
Height of the electric pole, h = AB = 10 m
Angle of elevation, θ = 45°
To find: Length of the wire, AC
Solution:
Let AB be the height of the electric pole and AC be the length of the wire.
In right angled Δ ABC,
cosec θ = [Hypotenuse] / [Opposite]
cosec 45° = AC/AB
Here θ = 45°
And also the opposite side is AB and the hypotenuse side is AC
AC = AB cosec 45°
Here AB = 10 m
= 10 × (√ 2) m
= 10 × 1.414 m
= 14.14 m
Therefore the length of the wire is 14.14 m.
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