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BITSAT 2022
Exam
BITSAT
Year
2022
Subject
Mathematics
Chapter
Heights and Distances

BITSAT 2022 · Mathematics · Heights and Distances

A house subtends a right angle at the window of a opposite house...

A house subtends a right angle at the window of a opposite house and the angle of elevation of the window from the bottom of the first house is 6060. If the distance between two houses be 6m6 \mathrm{ m}, then the height of the first house isA house subtends a right angle at the window of a opposite house and the angle of elevation of the window from the

Options

  1. A83m8 \sqrt{3} \mathrm{ m}
  2. B63m6 \sqrt{3} \mathrm{ m}
  3. C43m4 \sqrt{3} \mathrm{ m}
  4. DNone of these

Correct answer

A. 83m8 \sqrt{3} \mathrm{ m}

Step-by-step solution

Let PQP Q be the house subtending a right angle at the window BB of opposite house ABA B A house subtends a right angle at the window of a opposite house and the angle of elevation of the window from the
In △PAB\triangle P A B, we have tan⁡60∘=AB6=AB=63m\tan 60^{{}^{\circ}}=\frac{A B}{6}=A B=6 \sqrt{3} \mathrm{ m} In △CBQ\triangle C B Q, we have tan⁡30∘=h−CPBC\tan 30^{{}^{\circ}}=\frac{h-C P}{B C}⇒13=h−636[∵AB=CP,BC=AP]⇒h=6(3+13)⇒h=83m\begin{array}{ll}\Rightarrow & \frac{1}{\sqrt{3}}=\frac{h-6 \sqrt{3}}{6} \quad[\because A B=C P, B C=A P] \\ \Rightarrow & h=6\left(\sqrt{3}+\frac{1}{\sqrt{3}}\right) \\ \Rightarrow & h=8 \sqrt{3} \mathrm{ m}\end{array}$$
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