Class 10 Math Sample Paper 2019 | Q27A

This 2019 CBSE class 10 Maths 4 mark question is from Applications of Trigonometry. An 4-mark question in CBSE class 10 sample question paper. Concept tested: Trigonometry and speed, distance, and time.

Question 27A: A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how long will the car take to reach the observation tower from this point?

Video Explanation

Explanatory Answer

Let A be the man on top of the vertical observation tower.
The car takes 12 minutes to travel the distance BC.
The question is to find the time taken to travel the distance CD.

Consider ΔACD, ∠ACD = 45°
tan 45 = \\frac{AD}{CD})
1 = \\frac{AD}{CD})
CD = AD ------ (1)
Consider ΔABD, ∠ABD = 30°
tan 30 = \\frac{AD}{BD})
\\frac{1}{√3}) = \\frac{AD}{BC + CD})
BC + CD = √3 AD
BC + CD = √3CD [From (1) CD = AD]
BC = (√3 - 1)CD

Time taken to cover the distance BC = (√3 - 1)CD = 12 seconds
Time taken to cover the distance CD = \\frac{12}{(√3 − 1)})
= \\frac{12}{(√3 − 1)}) × \\frac{(√3 + 1)}{(√3 + 1)})
= \\frac{12(√3 + 1)}{3 − 1})
= 6(√3 + 1)