✓ Board-verified
Mathematics · 2022 · 3 marks
CBSE 2022 · Region 2 · Set 2 · Q9
Two men on either side of a cliff 75 m high observe the angles of elevation of the top of the cliff to be 30° and 60°. Find the distance between the…
Two men on either side of a cliff $\displaystyle 75$ m high observe the angles of elevation of the top of the cliff to be $\displaystyle 30$° and $\displaystyle 60$°. Find the distance between the two men.
Fig.
Fig.Marking-scheme solution
\[\begin{aligned}
\tan 30^{\circ}=\frac{1}{\sqrt{3}} & =\frac{75}{A C} \\
\Rightarrow A C & =75 \sqrt{3} \mathrm{~m} \ldots \ldots \ldots \text { (i) } \\
\tan 60^{\circ} & =\sqrt{3}=\frac{75}{A D} \\
\Rightarrow & A D=25 \sqrt{3} \text { m... ... ... (ii) }
\end{aligned}
\]
Adding (i) and (ii)
\[\begin{aligned}
C D & =(75 \sqrt{3}+25 \sqrt{3}) \mathrm{m} \\
& =100 \sqrt{3} \mathrm{~m}
\end{aligned}
\]
All Some Applications of Trigonometry questions2022 question paperNCERT solutions: Some Applications of TrigonometryPractice Some Applications of Trigonometry →
More from Some Applications of Trigonometry
- From the top of an 8 m high building, the angle of elevation of the top of a cable tower is 60^° and the angle of depression of its foot is 45^°.…2022
- From a point on the ground, which is 30 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be 60°.…2024
- From the top of a 45 m high light house, the angles of depression of two ships, on the opposite side of it, are observed to be 30° and 60°. If the…2024
- The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of…2022
- A boy standing on a horizontal plane is flying a kite with a string of length 60 m, at an angle of elevation of 30°. Another boy standing on the roof…2026
- Two boats are sailing in the sea 80 m apart from each other towards a cliff AB. The angles of depression of the boats from the top of the cliff are…2022
- The angle of elevation of the top of a building from a point A, on the ground, is 30°. On moving a distance of 24 m towards its base to the point B,…2026
- A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as 60^°. If AB=5 √3 m, then length of the wire…2026
CBSE Class 10 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.