SOLUTION: 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.

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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.
Found 3 solutions by Boreal, josmiceli, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Draw this, and the angles of the triangle of half of the parallelogram are 30.25 degrees, 116.85 degrees, and 33.2 degrees.
Law of Sines
sin 116.85/44.32=sin 30.2/side opposite. This is 0.0201=sin 30.2/side opposite, so side opposite is sin 30.2/0.0201=25.026 or 25.03 cm
The other side is 0.0201=sin 33.2/other side
the other side is sin 33.2/0.0201 or 27.24 cm
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = the 3rd angle





———————————
Angle is opposite the known sides,
so I can say:




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You can finish
Check he math and get a 2nd opinion if needed


Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
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.
 
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: . This should give you  , 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: . This should give you , the LONGER side.

These are the CORRECT lengths of the sides!
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