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If the angles of elevation of the top of the candle from two coins distant ‘a’ cm and ‘b’ cm (a > b) from its base and in the same straight line from it are 30° and 60° , then find the height of the candle.

If angles of elevation of top of candle from two coins distant a cm

Question 32 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 2
Question 32 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 3

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Question 32 If the angles of elevation of the top of the candle from two coins distant ‘a’ cm and ‘b’ cm (a > b) from its base and in the same straight line from it are 30° and 60° , then find the height of the candle. Let AB be the candle and let the height of candle be ℎ cm Given BD = a and BC = b In Δ ACD tan A = 𝐶𝐷/𝐴𝐶 tan 30° = h/a 1/√3 = h/a 𝒉 = 𝒂/√𝟑 In Δ BCD tan B = 𝐶𝐷/𝐵𝐶 tan 60° = h/b √3 = h/b 𝒉 = b√3 Multiplying (1) and (2) ℎ × ℎ = 𝒂/√𝟑 × b√3 ℎ^2 = ab 𝒉 = √𝒂𝒃 cm Hence, Height of the Candle= √𝑎𝑏 cm

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.