Example 3 - An observer 1.5 m tall is 28.5 m away from chimney - Questions easy to difficult

Example 3 - Chapter 9 Class 10 Some Applications of Trigonometry - Part 2
Example 3 - Chapter 9 Class 10 Some Applications of Trigonometry - Part 3

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Transcript

Example 3 An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney? Here, In diagram AB is chimney and CD is observer. Angle of elevation = 45° Hence, ∠ADE = 45° And, Distance (BC) = 28.5m Height of observer = CD = 1.5 m Since BC & DE are parallel lines BC = DE = 28.5 m Also, CD & BE are parallel lines & CD = BE = 1.5 m We have to find height of chimney = AB Since chimney is perpendicular to ground ∠ AED = 90° In right triangle AED, tan D = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐷)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐷) tan D = 𝐴𝐸/𝐷𝐸 tan 45° = 𝐴𝐸/𝐷𝐸 1 = 𝐴𝐸/28.5 1 × 28.5 = AE AE = 28.5m Now, AB = AE + BE AB = 28.5 + 1.5 AB = 30m Hence, Height of chimney = AB = 30 metre

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.