CBSE 10th Math Sample Paper 2019 | Q27B

This 2019 CBSE class 10 Maths 4 mark question is from Trigonometry. An 4 mark question from section D in CBSE class 10 sample question paper. A heights and distances important question.

Question 27B: The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30° and the angle of depression of its shadow from the same point in water of lake is 60°. Find the height of the cloud from the surface of water.

Video Explanation

Explanatory Answer

E is the point 60 m above the surface of water.
AB = h is the height of the cloud from the line of sight.
CD is the distance of reflection from the surface of water.
Let BE = x cm

Consider ΔABE, ∠E = 30°
tan 30 = \\frac{AB}{BE})
\\frac{1}{√3}) = \\frac{h}{x})
x = √3h ------ (1)

Consider ΔBDE, ∠E = 60°
tan 60 = \\frac{BD}{BE})
√3 = \\frac{h + 60 + 60}{x})
√3(√3h) = h + 120 [From (1) x = √3h]
2h = 120
h = 60