array l With usual notations, in triangle ABC , a= 3 +1, b= 3 -1 and m C =60^ , then A-B= array

Step-by-step solution

array l Given a = 3 +1, ~b = 3 -1, ~m C =60^ 60^ = ( 3 +1)²+( 3 -1)²- c ² 2( 3 +1)( 3 -1) 1 2 = 8- c ² 2(2) c ²=6 c = 6 By sine rule, a A = c C 3 +1 A = 6 60^ 3 +1 A = 6 ( 3 2 ) A = 3 2 ( 3 +1) 6 A = 3 +1 2 2 A =75^ or (180^ -75^ )=105^ B =180^ - (75^ +60^ )=45^ or 180^ - (105^ +60^ )=15^ By e rule, b B = c C 3 -1 B = 6 60^ B = 3 2 3 -1 6 = 3 -1 2 2 B =15^ or (180-15^ )=165^ Since B 165^ as C =60^ given, we take B =15^ B =15^ , A =105^ A - B =90^ array