Example 6 - Chapter 8 Class 10 Introduction to Trignometry (Important Question)

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Example 6 In Δ ABC, right-angled at B, AB = 5 cm and ∠ ACB = 30° (see Fig.). Determine the lengths of the sides BC and AC. Given AB = 5 cm & ∠ ACB = 30° According to diagram, tan C = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐶)/(𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐶) tan 30° = 𝑨𝑩/𝑩𝑪 1/√3=5/𝐵𝐶 BC = 5 √𝟑 cm sin C = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒 𝐶)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 sin 30° = 𝑨𝑩/𝑨𝑪 1/2=5/𝐴𝐶 AC = 10 cm Hence, AC = 10 cm & BC = 5 √3 cm

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