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An electric pole is 10 m high. A steel wire tied to the top of the pole is affixed at a point on the ground to keep the pole upright. If the wire makes an angle of 45° with the horizontal through the foot of the pole, find the length of the wire.

Heights & Distances

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Answer

Let MP be the pole and string is tied from point P on the pole to point O on the ground.

An electric pole is 10 m high. A steel wire tied to the top of the pole is affixed at a point on the ground to keep the pole upright. If the wire makes an angle of 45° with the horizontal through the foot of the pole, find the length of the wire. Heights and Distances, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Considering △POM,

∠PMO = 90°, ∠POM = 45° (given) and MP = 10 m.

From △POM, we get

⇒sin 45°=MPOP⇒12=10OP⇒OP=10×2⇒OP=10×1.414⇒OP=14.14\Rightarrow \text{sin 45°} = \dfrac{MP}{OP} \\[1em] \Rightarrow \dfrac{1}{\sqrt{2}} = \dfrac{10}{OP} \\[1em] \Rightarrow OP = 10 \times \sqrt{2} \\[1em] \Rightarrow OP = 10 \times 1.414 \\[1em] \Rightarrow OP = 14.14

Hence, the length of wire is 14.14 metres.

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