CBSE Class 10 Maths (Basic) 2025 · Paper 430(B)/S · Question 37

Some Applications of Trigonometry 4 marks Medium

An observer from the top of a

30

m tall lighthouse observes a ship at an angle of depression

3 0^{\circ}

coming towards the base of the lighthouse along a straight line joining the ship and the base of the lighthouse. The angle of depression changes to

4 5^{\circ}

after

10

seconds. Based on the above information, answer the following questions:

(i)Determine the distance of the ship from the base of the lighthouse, when the angle of depression is $3 0^{\circ}$ .[1]
(ii)Determine the distance of the ship from the base, after $10$ seconds from the initial position.[1]
(iii)(a)Find the distance between the two positions of the ship between $3 0^{\circ}$ and $4 5^{\circ}$ .[2]
(iii)(b)Find the speed of the ship between its two positions.[2]

Answer

(i) The distance is

303

\approx 51.96

m; (ii) The distance is

30

m; (iii)(a) The distance between the positions is

30 (3 - 1)

\approx 21.96

m; (iii)(b) The speed is

3 (3 - 1)

m/s

\approx 2.196

m/s.

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