Question 27 (Or 2nd) - CBSE Class 10 Sample Paper for 2019 Boards

Last updated at Oct. 1, 2019 by Teachoo

Question 27 (OR 2
nd
question)

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.

Question 27 (OR 2nd question)
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.
Here,
AB = 60 m
C is the point of the cloud
CF is the height of cloud from surface of water
Let CF = h m
FD is the shadow of cloud in water
So, FD = height of cloud = h m
And, Δ BEC & Δ BED are right angle triangles
Also, EF = AB = 60 m
Now,
In right triangle Δ BEC
tan B = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐵)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐵)
tan 30° = CE/BE
1/√3 = (ℎ − 60)/𝐵𝐸
BE = √3 (h – 60) m
Now,
In right triangle Δ BED
tan B = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐵)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐵)
tan 60° = 𝐸𝐷/BE
√3 = (ℎ + 60)/𝐵𝐸
√3 BE = h + 60
Putting BE = √3 (h – 60) from (1)
√3 × √3 (h – 60) = h + 60
3 (h – 60) = h + 60
3h – 180 = h + 60
3h – h = 60 + 180
2h = 240
h = 240/2
h = 120 m
So, height of Cloud = 120 m

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.