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

Last updated at April 16, 2024 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.

Transcript

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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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