Law of cosines problem? Help

In a rhombus whose side measures 24 and the smaller angle is 56°, find the length of the larger diagonal, to the nearest tenth.


i think i keep getting the wrong answer? i got 22.5

Form a right triangle with a rhombus side as the hypotenuse, half the long diagonal as the base and half the short diagonal as the vertical side. Then the angle opposite the short half-diagonal will be 56/2 = 28 degrees, and so the long half-diagonal D/2 will be such that cos(28) = (D/2)/24, and so

D = 48*cos(28) = 42.4.

You have used the wrong angle. You have found the shortest diagonal.
To find the largest diagonal you need the supplement of 56 - which is 124.
Draw a diagram - it will help.
Cheers.