Question 1122326
The diagonal of a parallelogram is 44.32 cm long and forms angles of 30°15' and 33°12' with the sides. Find the lengths of the two sides.
<pre>{{{system(matrix(1,4, 30^o, "15'", "=", 30.25^o), and, matrix(1,4, 33^o, "12'", "=", 33.2^o))}}} 
Use one of the parallelogram's 2 triangles formed from drawing the diagonal, and law of sines to find the SHORTER side of the parallelogram.
The equation for this is: {{{matrix(1,3, 44.32/sin (116.55^o), "=", matrix(1,2, Shorter, side)/sin (30.25^o)))}}}. This should give you  {{{highlight_green(matrix(1,2, 24.959, cm))}}}, the SHORTER side.


Use one of the parallelogram's 2 triangles formed from drawing the diagonal, and law of sines to find the LONGER side of the parallelogram. 
The equation for this is: {{{matrix(1,3, 44.32/sin (116.55^o), "=", matrix(1,2, Longer, side)/sin (33.2^o)))}}}. This should give you {{{highlight_green(matrix(1,2, 27.129, cm))}}}, the LONGER side.

These are the CORRECT lengths of the sides!</pre>