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Example 5 - In OPQ, OP = 7 cm and OQ - PQ = 1 cm. - Finding ratios when sides are given

Example 5 - Chapter 8 Class 10 Introduction to Trignometry - Part 2

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Example 5 In Δ OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm (see Fig.). Determine the values of sin Q and cos Q. In is given that in triangle OPQ, OQ – PQ = 1 cm OQ = 1 + PQ Using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 OQ2 = PQ2 + OP2 (1 + PQ)2 = PQ2 + (7)2 1 + PQ2 + 2PQ = PQ2 + 49 1 + PQ2 + 2PQ – PQ2 – 49 = 0 2PQ – 48 = 0 2PQ = 48 PQ = 48/2 PQ = 24 cm Also, OQ = 1 + PQ OQ = 1 + 24 OQ = 25 cm Now, sin Q = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑄)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 sin Q = 𝑂𝑃/𝑂𝑄 sin Q = 7/25

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.