CBSE Class 10 Maths (Basic) 2025 · Paper 430/3/1 · Question 37

Some Applications of Trigonometry 4 marks Medium

Case Study - 2: Two motorboats

A

and

B

are waiting at the opposite banks of a river in order to reach the opposite side. From a point

P

on the bridge,

20

m above the river, the angles of depression of the boats are

3 0^{\circ}

and

4 5^{\circ}

respectively, as shown in the figure given below. Both the boats leave at the same time at the speed of

10

m/s and

5

m/s, respectively. Based on the above information, answer the following questions:

iFind the distance travelled by boat $A$ to reach point $D$ in the river, vertically below the point $P$ . (Use $3 = 1.73$ )[1]
iiWhat is the width of the river?[1]
iii(a)Which boat will reach point $D$ first, and how much earlier than the other boat?[2]
iii(b)What is the distance between the two boats after $3$ seconds?[2]

Answer

(i) The distance travelled by boat A to reach

D

A D = 203 \approx 34.6

m. (ii) The width of the river is

A B = 34.6 + 20 = 54.6

m. (iii)(a) Boat A reaches

D

first,

4 - 3.46 = 0.54

s earlier than boat B. (iii)(b) After

3

s the boats are

54.6 - 45 = 9.6

m apart.

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