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NIMCET 2020 Mathematics PYQ — Angle of elevation of the top of the tower from 3 points (colline… | Mathem Solvex | Mathem Solvex

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NIMCET 2020 — Mathematics PYQ

NIMCET | Mathematics | 2020

Angle of elevation of the top of the tower from 3 points (collinear) A, B and C on a road leading to the foot of the tower are 30°, 45° and 60° respectively. The ratio of AB and BC is

Choose the correct answer:

A.
$3 : 1$
(Correct Answer)
B.
$3 : 2$

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C.
$1 : 2$

D.
$2 : 3$

Correct Answer:
$3 : 1$

Explanation

Concept:
If the angle of elevation from a point at distance D from tower of length L is θ
$tan θ = \frac{L}{D}$
Calculation:
Let the length of the tower OP be x

OA = $\frac{x}{t a n 30}$ = $3 x$

OB = $\frac{x}{t a n 45}$ = x

OC = $\frac{x}{t a n 60}$ = $\frac{x}{3}$

∴ AB = OA - OB = $3 x$ - x

BC = OB - OC = x - $\frac{x}{3}$

⇒ $\frac{A B}{B C}$ = $\frac{3 x - x}{x - \frac{x}{3}}$

⇒ $\frac{A B}{B C}$ = $\frac{3 ( x - 1 )}{3 - 1}$

⇒ $\frac{A B}{B C}$ = $3$ : 1

Explanation

Concept:
If the angle of elevation from a point at distance D from tower of length L is θ
$tan θ = \frac{L}{D}$
Calculation:
Let the length of the tower OP be x

If a number $x$ is selected at random from natural numbers 1,2,……,100,then …

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