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Mathematics · 2024 · 5 marks
CBSE 2024 · Region 5 · Set 3 · Q34
From a window 15 metres high above the ground in a street, the angles of elevation and depression of the top and the foot of another house on the…
From a window $\displaystyle 15$ metres high above the ground in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are $\displaystyle 30$° and $\displaystyle 45$° respectively. Find the height of the opposite house. (Use $\displaystyle \sqrt{3}=1 \cdot 732$ )
Marking-scheme solution
In right \(\displaystyle \Delta \mathrm{BPC}\), \(\displaystyle \tan 45^{\circ}=1=\frac{15}{x}\)
\[\Rightarrow x=15
\]
In right \(\displaystyle \Delta \mathrm{BPD}\), \(\displaystyle \tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{\mathrm{h}}{x}\)
\[\Rightarrow \quad \mathrm{h}=\frac{15 \sqrt{3}}{3} \text { or } 5 \sqrt{3}
\]
\[\begin{aligned}
\therefore \text { Height of opposite house }(\mathrm{CD}) & =5 \sqrt{3}+15 \\
& =5(1 \cdot 732)+15=23 \cdot 66 \mathrm{~m}
\end{aligned}
\]
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