The lengths of the three sides of a triangle (not necessarily a right triangle) are 3.10 meters, 8.03 meters and 9.29 meters. what is the cosine of the angle opposite the side of length 9.29 meters

The law of cosines tells you
.. 9.29^2 = 3.10^2 +8.03^2 -2*3.10*8.03*cos(angle)
.. cos(angle) = (9.29^2 -3.10^2 -8.03^2)/(-2*3.10*8.03)
.. cos(angle) ≈ -0.245314

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The angle is approximately arccos(-0.245314) ≈ 104.20039°, verified by a triangle solver.