Question

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

Answer 1

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.