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Example 5 - Observe figure and then find angle P. - Examples

  1. Class 10
  2. Important Questions for Exam - Class 10
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Example 5 Observe figure and then find ∠ P. Given: AB = 3.8 , PQ = 6√3 , BC = 6 , QR = 12 , AC = 3√3 , PR = 7.6 To find:- angle P i.e. ∠ P Solution:- in ∆ 𝐴𝐵𝐶 𝑎𝑛𝑑∆𝑅𝑄𝑃 Let us find the ratio of sides 𝐴𝐵/𝑅𝑄=3.8/7.6 = 38/76 = 1/2 𝐴𝐶/𝑅𝑃=(3√3)/(6√3)=1/2 𝐵𝐶/𝑄𝑃=6/12= 1/2 Thus, 𝐴𝐵/𝑅𝑄=𝐵𝐶/𝑄𝑃=𝐴𝐶/𝑅𝑃 (Using SSS similarity criterion) So , ∆ 𝐴𝐵𝐶 ~ ∆ 𝑅𝑄𝑃 Now we need to find ∠ P We know that corresponding angles of similar triangle are equal . Therefore, ∠ C = ∠ P In ∆ 𝐴𝐵𝐶 ∠ A + ∠ B + ∠ C = 180° 80°+60° + ∠ C = 180° 140° + ∠ C = 180° ∠ C = 180°−140° ∠ C = 40° Thus, ∠ C = 40° Hence , ∠ P = ∠ C = 40°

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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