Final answer:
To find the measure of angle J in triangle JKL, the Law of Cosines is used with the given side lengths, yielding an angle measure of approximately 95 degrees for m∠J.
Step-by-step explanation:
The question is asking to find the measure of angle J in triangle JKL with the given side lengths j = 10 inches, k = 7 inches, and l = 6.58 inches. To solve this, we can use the Law of Cosines which relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, to find m∠J, we can set up the equation:
cos(J) = (k^2 + l^2 - j^2) / (2 * k * l)
Plugging in the values:
cos(J) = (7^2 + 6.58^2 - 10^2) / (2 * 7 * 6.58) = (-7.68) / (92.28) ≈ -0.0832
Now, we can find the angle J by calculating the inverse cosine (also known as arccosine) of -0.0832:
J = arccos(-0.0832)
After calculating, we find that m∠J is approximately 95 degrees. Therefore, the correct answer is 95°.