In ΔJKL, j = 10 in., k = 7 in., and l = 6.58 in. Find m∠J.

Answer 1

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.