Question

A traingle has an area 48sqaure cm and its shorter sides have lenghts 9 cm and 12cm. Find the largest angle of the triangle

Answer 1

Looks like the same question posted by "Tareena"

So here is the same answer:

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:
(Broken Link Removed)

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.

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.