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NIMCET 2023 Mathematics PYQ — A line segment AB of length 10 meters is passing through the foot… | Mathem Solvex | Mathem Solvex

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NIMCET 2023 — Mathematics PYQ

NIMCET | Mathematics | 2023

A line segment AB of length 10 meters is passing through the foot of the perpendicular of a pillar, which is standing at right angle to the ground. Tip of the pillar subtends angles tan $^{- 1}$ 3 and tan $^{- 1}$ 2 at A and B respectively Which ofthe following choice represents the height ofthe pillar?

Choose the correct answer:

A.
10 meter
B.
8 meter
C.
12 meter
(Correct Answer)
D.
15 meter

Correct Answer:

12 meter

Explanation

Let $α = tan^{- 1} 3 \Rightarrow tan α = 3$ and $β = tan^{- 1} 2 \Rightarrow tan β = 2$

In $△ A P Q$

$tan α = \frac{h}{x} = 3 \Rightarrow x = \frac{h}{3}$

In $△ B P Q$

$tan β = \frac{h}{10 - x} = 2 \Rightarrow h = 20 - 2 x$

$\Rightarrow h = 20 - 2 h /3$

$\Rightarrow h = 12$

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Explanation

Let $α = tan^{- 1} 3 \Rightarrow tan α = 3$ and $β = tan^{- 1} 2 \Rightarrow tan β = 2$

In $△ A P Q$

$tan α = \frac{h}{x} = 3 \Rightarrow x = \frac{h}{3}$

In $△ B P Q$

$tan β = \frac{h}{10 - x} = 2 \Rightarrow h = 20 - 2 x$

$\Rightarrow h = 20 - 2 h /3$

$\Rightarrow h = 12$

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