JEE Main 2015 · 4 Apr · Shift 1 · Mathematics Q88

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MathematicsSingle correct+4 / -1Question 88 of 90

If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30°, 45° and 60° respectively, then the ratio, AB : BC, is :

\sqrt3:1

\sqrt3:\sqrt2

1:\sqrt3

2 : 3

Answer and worked solution

Official answer: A

With tower height $h$ , the distances from the foot are $h\sqrt3$ , $h$ and $\dfrac h{\sqrt3}$ . So $AB=h(\sqrt3-1)$ and $BC=h\left(1-\frac1{\sqrt3}\right)=\dfrac{h(\sqrt3-1)}{\sqrt3}$ .

$AB:BC=\sqrt3:1$ .

Topics:Heights and distances

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JEE Main 2015 · 4 Apr · Shift 1, Mathematics question 88