CBSE Class 10 Maths (Standard) 2025 · Paper 30/4/1 · Question 38

Some Applications of Trigonometry 4 marks Hard

A drone was used to facilitate movement of an ambulance on the straight highway to a point P on the ground where there was an accident. The ambulance was travelling at the speed of

60

km/h. The drone stopped at a point Q,

100

m vertically above the point P. The angle of depression of the ambulance was found to be

3 0^{\circ}

at a particular instant. Based on above information, answer the following questions: (Use

3 = 1.73

)

(i)Represent the above situation with the help of a diagram.[1]
(ii)Find the distance between the ambulance and the site of accident (P) at the particular instant.[1]
(iii)(a)Find the time (in seconds) in which the angle of depression changes from $3 0^{\circ}$ to $4 5^{\circ}$ .[2]
(iii)(b)OR — How long (in seconds) will the ambulance take to reach point P from a point T on the highway such that angle of depression of the ambulance at T is $6 0^{\circ}$ from the drone?[2]

Answer

(i) The diagram is right

△ QP R

in the figure, with

∠ S QR = 3 0^{\circ}

Q

; (ii) At that instant the ambulance is

1003 = 173

m from

P

; (iii)(a) The angle changes from

3 0^{\circ}

4 5^{\circ}

\frac{219}{50} = 4.38

s; (iii)(b) The ambulance takes

23 \approx 3.46

s to reach

P

from

T

🔒 Step-by-step solution

From the board paper

CBSE Class 10 Maths (Standard) 2025 · Paper 30/4/1, Question 38 — all 38 questions with answers →

CBSE Class 10 Maths (Standard) 2025 · Paper 30/4/1 · Question 38

Answer

From the board paper

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