<prompt> Determine the angle measures of the given triangle.Side lengths: 14, 3, 15  <response>: According to the problem, the triangles side lengths are 14, 3, and 15 units. Because 15 is the largest side, we can apply the Law of Cosines to find the angle opposite of 15. Let it be angle C. The other angles can be called A and B.Let a14, b3, c15, thencosC a2 b2 - c2 2ab 142 32 - 152 2 14 3 -0.3571428571C arccos-0.3571428571 111.8Now, to find angle A, we can use Law of Sines, which states that the ratio of the measure of one of a triangles angles to the length of the side opposite that angle is the same for all three angles of the triangle.Thus,asinA csinC 14sinA 15sin111.8Solving for sinA, we find sinA 14 sin111.815 0.9235687435Hence, A arcsin0.9235687435 67.4To find angle B we can use that the sum of the angles of the triangle is 180, thenA B C 180 B 180 A C 180 67.4 111.8 0.8Therefore, the angle measures of the given triangle are 67.4, 0.8, and 111.8. 