A pole on the ground leans at 60° with the vertical. At a point x metre away from the base of the pole on the ground, two halves of the pole subtend the same angle. If the pole and the point are in the same vertical plane, then what is the length of the pole?
A pole on the ground leans at 60° with the vertical. At a point x metre away from the base of the pole on the ground, two halves of the pole subtend the same angle. If the pole and the point are in the same vertical plane, then what is the length of the pole? Correct Answer <span class="math-tex">\(\sqrt 3 x\)</span> metre
Calculation:
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⇒ Let length of pole be AB metre.
⇒ ∠ ACD and ∠ BCD = ∠m
BD = DA, as D is the midpoint of AB
Δ ADC and Δ BDC are congruent triangles.
⇒ ∠ ADC = ∠ BDC
⇒ ∠ ADC + ∠ BDC = 180 ......(Linear pair angles)
⇒ ∠ ADC + ∠ BDC = 90
In Δ BDC,
⇒∠ BCD = m = 180 - 90 - 30 = 60
⇒ sin 60 = BD/x
⇒ BD = √3x/2
⇒ AB = 2BD = √3x
∴ Length of pole is √3x metre.
