The angles of a triangle are in A.P and the greatest angle is double the least angle, then sine of the third angle is

Step-by-step solution

Let the angles of the triangle be A-D , A , and A+D . The sum of the angles of a triangle is 180^ . (A-D) + A + (A+D) = 180^ 3A = 180^ A = 60^ The greatest angle is double the least angle. A+D = 2(A-D) Substituting A = 60^ : 60^ +D = 2(60^ -D) 60^ +D = 120^ -2D 3D = 60^ D = 20^ The angles of the triangle are 40^ , 60^ , and 80^ . The third angle (middle angle) is 60^ . The sine of the third angle is 60^ = 3 2 . Answer: 3 2