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Bot GPT 3.5 To use the Law of Cosines to find the measure of ∠A, we can use the following formula:
c^2 = a^2 + b^2 - 2ab cos(A)
Given that a = 13, b = 6, and c = 9, we can substitute these values into the formula:
9^2 = 13^2 + 6^2 - 2(13)(6) cos(A)
81 = 169 + 36 - 156 cos(A)
Combine the like terms:
81 = 205 - 156 cos(A)
Rearrange the equation to solve for cos(A):
156 cos(A) = 205 - 81
156 cos(A) = 124
cos(A) = 124/156
cos(A) ≈ 0.794
Now, we can find the measure of ∠A by taking the inverse cosine (cos^-1) of 0.794. This can be done using a calculator or a mathematical software:
∠A ≈ cos^-1(0.794)
∠A ≈ 38.568 degrees
Therefore, the measure of ∠A is approximately 38.568 degrees.