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) About Me  (Show Source):
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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) About Me  (Show Source):
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Let +alpha+ = the 3rd angle
+30+%2B+15%2F60+%2B+33+%2B+12%2F60+%2B+alpha+=+360+
+63+%2B+27%2F60+%2B+alpha+=+360+
+alpha+=+360+-+63+-+27%2F60+
+alpha+=+297+-+.45+
+alpha+=+296.55+
———————————
Angle +alpha+ is opposite the known sides,
so I can say:
+44.32%2Fsin%28+296.55+%29+=+b%2Fsin%28+30.25+%29+
+44.32%2F-.8945+=+b%2F.50378+
+-49.5472+=+b%2F.50378+
+b+=+-24.961+
————————————
+-49.5472+=+c%2Fsin%28+33.2+%29+
You can finish
Check he math and get a 2nd opinion if needed


Answer by MathTherapy(10555) About Me  (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  highlight_green%28matrix%281%2C2%2C+24.959%2C+cm%29%29, 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 highlight_green%28matrix%281%2C2%2C+27.129%2C+cm%29%29, the LONGER side.

These are the CORRECT lengths of the sides!