✓ Board-verified
Mathematics · 2022 · 3 marks
CBSE 2022 · Region 2 · Set 3 · Q8
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°. If the bridge is at a…
From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $\displaystyle 30$° and $\displaystyle 45$°. If the bridge is at a height of $\displaystyle 8$ m from the banks, then find the width of the river.
Marking-scheme solution
\[\begin{array}{r}
\tan 45^{\circ}=\frac{8}{B C}=1 \\
\Rightarrow B C=8 \mathrm{~m} \\
\tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{8}{C D} \\
\Rightarrow C D=8 \sqrt{3} \mathrm{~m}
\end{array}
\]Adding equations, $\displaystyle \mathrm{BD}=B C+C D=8(\sqrt{3}+1) m$
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.