A triangular field has sides of lengths 21, 39, and 41 yd. Find the largest angle. (Round your answer to the nearest degree.)

Question

Josiah

Mathematics

12 December, 02:58

A triangular field has sides of lengths 21, 39, and 41 yd. Find the largest angle. (Round your answer to the nearest degree.)

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Answers (1)

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Mila Cooke · Answer 1

80 degrees

Step-by-step explanation:

To start, use the fact that the largest angle is the opposite of the longest side. Now, use the Law of Cosines (a^2 = b^2 + c^2 - 2bc cos A), where a is the longest side and A is its opposite, and b and c are the other sides. Plug the values in to get 1681 = 1962 - 1638 cos A, or cos A = 281 / 1638. Now, use a calculator to get that A is approximately 80.12 degrees, or 80 degrees.