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.

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  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

Transcript

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
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.