# The two sides of the triangle are 13m and 7m, and the angle opposite to the larger one is 60 °.

September 23, 2021 | education

| **The two sides of the triangle are 13m and 7m, and the angle opposite to the larger one is 60 °. Find the third side of the triangle.**

Let ABC be a given triangle, AC = 13 m, AB = 7 m, ∠ABS = 60 °.

Let side BC = y cm.

According to the cosine theorem, AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * cos60 °.

169 = 49 + y ^ 2 – 2 * 7 * y * ½;

y ^ 2 – 7y – 120 = 0.

D = 49 + 4 * 120 = 529 = 232.

y1 = (7 – 23) / 2 = – 16/2 = – 8 (does not fit, since the length cannot take negative values),

y2 = (7 + 23) / 2 = 30/2 = 15 (m).

Answer: the third side of the triangle is 15 m.