NIMCET 2023 Question Paper with solutions

Question : 6 of 120

Marks: +1, -0

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 of the following choice represents the height of the pillar?

15 meter
12 meter
10 meter
8 meter

Validate

Solution:

\;\;\text " Let "\; α=\tan ^{-1} 3

⇒ \;\; \tan α=3 \;\text " and "\; β=\tan ^{-1} 2

⇒ \tan β=2

△ {\APQ}, \;\; \tan α=\;{h}/{x}=3 ⇒ x=\;{h}/{3}

\;\text " In "\; △ {\BPQ},\;\tan β\;=\;{h}/{10-x}=2

⇒\;h\;=20-2 x

⇒ h\;=20-2 h \/ 3

⇒ h\;=12 .

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