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, 4 Given 15 cot A = 8, find sin A and sec A. Given 15 cot A = 8 cot A = ๐/๐๐ Now, tan A = 1/cotโก๐ด = 1/(8/15) = ๐๐/๐ Now, tan A = 15/8 (๐ ๐๐๐ ๐๐๐๐๐ ๐๐ก๐ ๐ก๐ โ ๐ด)/(๐ ๐๐๐ ๐๐๐๐๐๐๐๐ก ๐ก๐โ ๐ด) = 15/8 ๐ฉ๐ช/๐จ๐ฉ=๐๐/๐ Let BC = 15x & AB = 8x Finding AC Using Pythagoras theorem, (Hypotenuse)2 = (Height)2 + (Base)2 AC2 = AB2 + BC2 AC2 = (8x)2 + (15x)2 AC2 = 64 x2 + 225 x2 AC2 = 289 x2 AC2 = (17x)2 AC = 17x Now, we need to find sin A & sec A sin A = (๐ ๐๐๐ ๐๐๐๐๐ ๐๐ก๐ ๐ก๐ โ ๐ด)/๐ป๐ฆ๐๐๐ก๐๐๐ข๐ ๐ = ๐ต๐ถ/๐ด๐ถ = 15๐ฅ/17๐ฅ = ๐๐/๐๐ For sec A , Finding cos A first cos A = (๐ ๐๐๐ ๐๐๐๐๐๐๐๐ก ๐ก๐ โ ๐ด)/๐ป๐ฆ๐๐๐ก๐๐๐ข๐ ๐ = ๐ด๐ต/๐ด๐ถ = 8๐ฅ/17๐ฅ = ๐/๐๐ And, sec A = 1/cosโกใ ๐ดใ = 1/(8/17) = ๐๐/๐