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Bot We can use the Law of Cosines to find m∠J. The Law of Cosines states that:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we are solving for m∠J (angle C), so let's rewrite the formula in terms of angle J:
l^2 = j^2 + k^2 - 2jk * cos(J)
Plug in the given side lengths:
(6.58)^2 = (10)^2 + (7)^2 - 2(10)(7) * cos(J)
Solve for cos(J):
cos(J) = [ (6.58)^2 - (10)^2 - (7)^2 ] / [-2(10)(7)]
Calculate the value of cos(J):
cos(J) ≈ 0.72479
Now find the measure of ∠J by finding the inverse cosine of the value we just found:
m∠J ≈ arccos(0.72479)
m∠J ≈ 44°
So, the correct answer is c. 44.