In ABC , if a =2, ~B = ⁻¹ 1 2 and C= ⁻¹ 1 3 , then (A, b) equals

Step-by-step solution

Given that, a =2 In ABC , B = ⁻¹ ( 1 2 ) C= ⁻¹ ( 1 3 ) We know that in ABC , A+B+C= A = - B - C A = - ⁻¹ ( 1 2 )- ⁻¹ ( 1 3 ) A = - ⁻¹ ( 1 2 + 1 3 1- 1 6 ) A = - ⁻¹ ( 5 / 6 5 / 6 )= - ⁻¹(1) A = - ⁻¹ ( 4 ) A = - 4 A = 3 4 Now, A= 3 4 aligned =& 135^ = 45^ = 1 2 B &= 1 5 ( B = 1 2 ) aligned Now, by sine law gathered a A = b B b = a B A =2 1 5 1 2 = 2 2 5 gathered Hence, (A, b)= 3 4 , 2 2 5