Finding ratios when other ratios are given
Finding ratios when other ratios are given
Last updated at April 16, 2024 by Teachoo
Ex 8.1, 3 If sin A = 3/4 , calculate cos A and tan A. Given sin A = 3/4 (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 ∠𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 3/4 𝑩𝑪/𝑨𝑪 = 𝟑/𝟒 Let BC = 3x AC = 4x We find AB using Pythagoras Theorem In right triangle ABC Using Pythagoras theorem Hypotenuse2 = Height2 + Base2 AC2 = AB2 + BC2 (4x)2 = AB2 + (3x)2 16x2 = AB2 + 9x2 16x2 – 9x2 = AB2 7x2 = AB2 AB2 = 7x2 AB = √7𝑥2 AB = √𝟕 x Now, we need to find cos A & tan A cos A = (𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 ∠ 𝐴)/𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 𝐴𝐵/𝐴𝐶 = (√𝟕 𝒙)/𝟒𝒙 = √𝟕/𝟒 tan A = (𝑠𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 ∠𝐴)/(𝑠𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜∠𝐴) = 𝐵𝐶/𝐴𝐵 = 𝟑𝒙/(√𝟕 𝒙) = 𝟑/√𝟕