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Mathematics · 2024 · 5 marks
CBSE 2024 · Region 1 · Set 2 · Q33
From the top of a building $\displaystyle 60$ m high, the angles of depression of the top and bottom of the vertical lamp post are observed to be $\displaystyle 30^{\circ}$ and $\displaystyle 60^{\circ}$ respectively.(i)Find the horizontal distance between the building and the lamp post.(ii)Find the distance between the tops of the building and the lamp post.
From the top of a building $\displaystyle 60$ m high, the angles of depression of the top and bottom of the vertical lamp post are observed to be $\displaystyle 30^{\circ}$ and $\displaystyle 60^{\circ}$ respectively.
(i)
Find the horizontal distance between the building and the lamp post.
(ii)
Find the distance between the tops of the building and the lamp post.
Marking-scheme solution
Let AB be the building and CD be the lamp post of height 'h' m.(i) \(\displaystyle \tan 60^{\circ}=\sqrt{3}=\frac{60}{x}\)
\[\Rightarrow x=20 \sqrt{3} \mathrm{~m}
\]
\[\text { or } \mathrm{AC}=20 \sqrt{3} \mathrm{~m}
\]
(ii) \(\displaystyle \cos 30^{\circ}=\frac{\sqrt{3}}{2}=\frac{x}{\mathrm{BD}}\)
\[\Rightarrow \mathrm{BD}=\frac{2 \times 20 \sqrt{3}}{\sqrt{3}}=40 \mathrm{~m}
\]
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