Given that cosA = 5/12

Since we know that from Pythagoras theorem,

 hypotenuse² = base² + perpendicular²

=>12² = 5² + perpendicular²

=> 144 = 25 + perpendicular²

=> 144-25 = perpendicular²

=> 119 = perpendicular²

=>perpendicular = √119

Now  sin A = √119/12

Again sin2A = 2*sinA*cosA

                  = 2*√119/12*5/12

                  = (2*√119*5)/(12*12)

                  = (√119*5)/(6*12)

                  = (5*√119)/72