The Statue of Unity situated in Gujarat is the world's largest Statue which stands over a 58 m high base. As part of…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 4 Marks · March 2025 · Standard
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314 Marks · March 2025 · Standard
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 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 $80\sqrt{3}$ m away from the base of the Statue is found to be $60^\circ$. Situation - II: The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be $30^\circ$ and entire height of the Statue including the base is found to be 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 (iii) (b) Find the horizontal distance of point B (Situation - II) from the Statue and the value of $\tan \alpha$, where $\alpha$ is the angle of elevation of top of base of the Statue from point B.
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(i) Correct figure (1 mark). (ii) Correct figure (1 mark). (iii) (a) In $\Delta ACQ$, $\frac{QC}{AC} = \tan 60^\circ = \sqrt{3} \Rightarrow QC = 240$ m. Height of statue including base = 240 m. Height of statue excluding base = $240 - 58 = 182$ m (1 + 1 marks). OR (iii) (b) $QR = 240 - 40 = 200$ m. In $\Delta QRB$, $\frac{QR}{RB} = \tan 30^\circ = \frac{1}{\sqrt{3}}$. Horizontal distance $RB = 200\sqrt{3}$ m ($\frac{1}{2} + \frac{1}{2}$ marks). Correct figure ($\frac{1}{2}$ mark). In $\Delta PRB$, $\tan \alpha = \frac{PR}{BR} = \frac{18}{200\sqrt{3}}$ or $\frac{3\sqrt{3}}{100}$ ($\frac{1}{2}$ mark).
