SOLUTION: Hi I've tried but I can't even get the picture and I appreciate this! the lengths of two sides and one diagonal of a parrellelogram and 8m, 13m, and 20m, respectively. what is the

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Question 574123: Hi I've tried but I can't even get the picture and I appreciate this! the lengths of two sides and one diagonal of a parrellelogram and 8m, 13m, and 20m, respectively. what is the measure of each angle of the parallelogram? Thanks!
Answer by KMST(5396) About Me  (Show Source):
You can put this solution on YOUR website!
There is your picture. I completed the parallelogram in green, so you can see it, but you are concerned with just the half of the parallelogram that I drew as a black triangle.
Since you know only the length of all three sides of the triangle, you are forced to use law of cosines to solve it. Applied to this triangle, law of cosines says that:
8%5E2%2B13%5E2-2%2A8%2A13%2Acos%28A%29=20%5E2 --> 64%2B169-208cos%28A%29=400 --> cos%28A%29=%28400-64-169%29%2F%28-208%29 --> cos%28A%29=-167%2F208 --> A=2.503 radians or A=143.4%5Eo
In a parallelogram, the opposite angle (green in this case) is congruent, so it has the same measure.
The other two angles are supplementary, so their measure is
180%5Eo-143.4%5Eo=36.6%5Eo