Final answer:
Using the Law of Cosines with the given side lengths of triangle AJKL, we find that the measure of angle L is approximately 74.73 degrees, which is not one of the provided multiple choice answers. This suggests there might be an error in the question or the provided options.
Step-by-step explanation:
To find the measure of angle L in triangle AJKL, we can use the Law of Cosines since the lengths of all three sides are known. The Law of Cosines states that for any triangle with sides of lengths a, b, and c, and opposite angles A, B, and C, respectively, the following relationship holds true:
Cos(C) = (a^2 + b^2 - c^2) / (2ab)
Let's assign the sides as follows: j = 9 cm (side a), k = 6.2 cm (side b), and l = 9.5 cm (side c). We want to find angle L (angle C), which lies opposite to side l. Substituting the values we have:
Cos(L) = ((9)^2 + (6.2)^2 - (9.5)^2) / (2 * 9 * 6.2)
Cos(L) = (81 + 38.44 - 90.25) / (2 * 9 * 6.2)
Cos(L) = (29.19) / (111.6)
Cos(L) \u2248 0.2615
Now, to find angle L, we take the inverse cosine (arc cos) of 0.2615:
L = Cos^{-1}(0.2615)
Calculating this gives us the measure of angle L. Upon using a calculator, we find that angle L is approximately 74.73 degrees. This is not one of the options provided in the question, indicating that there might have been a typo or an error in the question or the available answers.