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.

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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

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.