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Mathematics · 2025 · 4 marks
CBSE 2025 · Region 6 · Set 1 · Q38
The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a 58 m high base. As part of the project, a student…
The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a $\displaystyle 58$ m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places : Situation - I : The angle of elevation of the top of Statue from Place A which is $\displaystyle 80 \sqrt{3} \mathrm{~m}$ away from the base of the Statue is found to be $\displaystyle 60$°. Situation - II : The angle of elevation of the top of Statue from a Place B which is $\displaystyle 40$ m above the ground is found to be $\displaystyle 30$° and entire height of the Statue including the base is found to be $\displaystyle 240$ m.
Based on given information, answer the following questions :
(i)
Represent the Situation - I with the help of a diagram.
(ii)
Represent the Situation - II with the help of a diagram.
(iii)
(a)
Calculate the height of Statue excluding the base and also find the height including the base with the help of Situation - I.
OR
(b)
Find the horizontal distance of point B (Situation - II) from the Statue and the value of $\displaystyle \tan \alpha$, where $\displaystyle \alpha$ is the angle of elevation of top of base of the Statue from point B.
Marking-scheme solution
(iii)
In $\displaystyle \triangle \mathrm{ACQ}$
\[\frac{\mathrm{QC}}{\mathrm{AC}}=\tan 60^{\circ}=\sqrt{3}
\]
\[\mathrm{QC}=240 \mathrm{~m}
\]
Height of statue including base $\displaystyle =240 \mathrm{~m}$
Height of statue excluding base $\displaystyle =240-58=182 \mathrm{~m}$
\[\mathrm{QR}=240-40=200 \mathrm{~m}
\]
In $\displaystyle \triangle \mathrm{QRB}$
\[\frac{\mathrm{QR}}{\mathrm{RB}}=\tan 30^{\circ}=\frac{1}{\sqrt{3}}
\]
Horizontal distance $\displaystyle \mathrm{RB}=200 \sqrt{3} \mathrm{~m}$
In $\displaystyle \triangle \mathrm{PRB}$
\[\begin{aligned}
\tan \alpha & =\frac{\mathrm{PR}}{\mathrm{BR}} \\
& =\frac{18}{200 \sqrt{3}} \text { or } \frac{3 \sqrt{3}}{100}
\end{aligned}
\]
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