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.     Subscribe to our Youtube Channel - https://you.tube/teachoo

1. Class 10
2. Solutions of Sample Papers for Class 10 Boards
3. CBSE Class 10 Sample Paper for 2019 Boards

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

CBSE Class 10 Sample Paper for 2019 Boards

Class 10
Solutions of Sample Papers for Class 10 Boards 