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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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. Given in Δ 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 cos Q = (𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝑄)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠 cos Q = 𝑃𝑄/𝑂𝑄 cos Q = 𝟐𝟒/𝟐𝟓

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Davneet Singh

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.