The two sides of the triangle are 27.4 and 16.3, and the angle between them is 140 degrees. Find the third side

1. There is a known formula for finding the third side of a triangle when its two sides and the angle between them are known.

a ^ 2 = b ^ 2 + c ^ 2 – 2 * b * c * cos A.

2. By the condition of the problem, the sides of the triangle b = 27.4, c = 16.3 are known, and the angle A between the sides is 140 °.

Using the formula and the value from the table cos 140 ° = – 0.766, we calculate the side a of the triangle.

a ^ 1/2 = (27.4 ^ 2 + 16.3 ^ 2 + 2 * 27.4 * 16.3 * 0.766) ^ 1/2 = (750.76 + 265.7 + 893.24 * 0.766 ) ^ 1/2 = (750.76 + 265.7 + 684.22) ^ 1/2 = 1700.7 ^ 1/2 = 41.

Answer: In a triangle, side a is 41.