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18/01/2022 1:17 pm
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Two poles, AB of length a metres and CD of length a + b (b ≠ a) metres are erected at the same horizontal level with bases at B and D. If BD = x and tan ACB = 1/2, then:
(1) x2 + 2(a + 2b)x - b(a + b) = 0
(2) x2 + 2(a + 2b)x + a(a + b) = 0
(3) x2 – 2ax + b(a + b) = 0
(4) x2 – 2ax + a(a + b) = 0
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18/01/2022 1:24 pm
Correct answer: (3) x2 – 2ax + b(a + b) = 0
Explanation:
tan θ = \(\frac{1}{2}\)
tan(θ + α) = \(\frac{x}{b}\), tan α = \(\frac{x}{a +b}\)
⇒ \(\frac{1}{2}\) + \(\frac{x}{a +b}\)
⇒ \(\frac{\frac{1}{2}+ \frac{x}{a +b}}{1 - \frac{1}{2} \times \frac{x}{a+b}}\) = \(\frac{x}{b}\)
⇒ x2 – 2ax + ab + b2 = 0