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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 2 · Set 1 · Q24
(a) The length of the shadow of a tower on the plane ground is √ 3 times the height of the tower. Find the angle of elevation of the sun.
(a)
The length of the shadow of a tower on the plane ground is $\displaystyle \sqrt{3}$ times the height of the tower. Find the angle of elevation of the sun.
OR
(b)
The angle of elevation of the top of a tower from a point on the ground which is $\displaystyle 30$ m away from the foot of the tower, is $\displaystyle 30$°. Find the height of the tower.
Marking-scheme solution
Let AB be the tower of height 'h'.
\[\therefore \mathrm{AC}=\sqrt{3} \mathrm{~h}
\]
In \(\displaystyle \triangle \mathrm{ABC}, \tan \theta=\frac{\mathrm{AB}}{\mathrm{AC}}=\frac{\mathrm{h}}{\sqrt{3} \mathrm{~h}}\)
\[\begin{aligned}
& \Rightarrow \tan \theta=\frac{1}{\sqrt{3}} \\
& \Rightarrow \theta=30^{\circ}
\end{aligned}
\]
Height of tower = AB
In \(\displaystyle \triangle \mathrm{ABC}, \tan 30^{\circ}=\frac{\mathrm{AB}}{30}\)
\[\Rightarrow \mathrm{AB}=\frac{30}{\sqrt{3}}=10 \sqrt{3}
\]
∴ Height of Tower is \(\displaystyle 10 \sqrt{3} \mathrm{~m}\)
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