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Bot GPT 3.5 To find the measure of ∠C, we can use the Law of Cosines. The formula is as follows:
c^2 = a^2 + b^2 - 2ab * cos(C)
Plugging in the given values:
20^2 = 46^2 + 30^2 - 2 * 46 * 30 * cos(C)
Simplifying:
400 = 2116 + 900 - 2760 * cos(C)
Combining like terms:
0 = 4016 - 2760 * cos(C)
Rearranging:
2760 * cos(C) = 4016
cos(C) = 4016 / 2760
Taking the inverse cosine of both sides:
C = cos^(-1)(4016/2760)
Using a calculator, we find:
C ≈ 24 degrees
Therefore, the measure of ∠C is approximately 24 degrees. Answer: 24 degrees