# Math

a traingle has an area 48 square cm and its shorter sides have lengths 9cm and 12cm. find the lagest angle of the traingle.

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1. I first solved this by iteration. (trying different angles between the two given sides until I got the correct area).
I used a tool that I found here:

I got the third side length to be 11.227 and the angle opposite the side with length 12 to be 71.82 degrees. The other two angles are 45.44 and 62.73 degrees. So the answer is 71.82 degrees

Here is better way to do it:
One can get an area of 48 if the altitude of the triangle measured from the side of length 12 is 8. With that information, you can reconstruct the full triangle. The sine of the angle between the sides of length 9 and 12 is 8/9, so that angle is 62.73 degrees. The law of cosines can now be used for the third side length (11.227). The law of sines can be used for either one of the remaining angles.

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