In a triangle ABC AB = 4 BC = √37 AC = 3 Find the degree measure of the larger angle of the triangle.

Let’s solve this problem. In a triangle, the largest angle is opposite the largest side. The largest side BC = √ 37. Therefore, the largest angle A

Let’s use the cosine theorem to solve:

cos A = (AC ^ 2 + AB ^ 2 – BC ^ 2) / (2 * AC * AB).

Let’s substitute the values of the sides:

cos A = (3 ^ 2 + 4 ^ 2 – (√ 37) ^ 2) / (2 * 4 * 3) = (9 + 16 – 37) / 24 = – 12/24 = – 0.5.

To determine the degree measure of the angle, we will use the Bradis table. сos A = – 0.5, which corresponds to an angle of 240 °.

Answer: The largest angle is 240 °.