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To find angle J, we can use the Law of Cosines since we are given the lengths of all three sides.
The Law of Cosines is given by:
c^2 = a^2 + b^2 - 2ab * cos(C)
where a, b, and c are the lengths of the three sides, and C is the angle opposite side c.
Plugging in the values we have:
10^2 = 7^2 + 6.58^2 - 2(7)(6.58) * cos(J)
Solving for cos(J):
100 = 49 + 43.2164 - 91.88 * cos(J)
100 = 92.2164 - 91.88 * cos(J)
91.880 * cos(J) = -8.2164
cos(J) = -8.2164 / 91.880
cos(J) = -0.0894
Now, to find angle J, we take the inverse cosine of -0.0894:
J = cos^(-1)(-0.0894)
J ≈ 94.41 degrees
Therefore, m∠J ≈ 94.41 degrees.