The sides of the triangle are proportional to the numbers 7, 8, 13. Find the largest angle if its perimeter is 56cm.

Let’s designate this triangle ABC. We introduce the coefficient of proportionality x and we get:
AB = 7x;
BC = 8x;
AC = 13.
The perimeter of the condition is 56 cm, we draw up the equation:
7x + 8x + 13x = 56
28x = 56
x = 2.
The sides of the triangle are equal:
AB = 7 * 2 = 14 (cm);
BC = 8 * 2 = 16 (cm);
AC = 13 * 2 = 26 (cm).
The larger angle is opposite the larger side of the AC and this is the ABC angle. To find it, we use the cosine theorem:
Cos ABC = (AB² + BC² – AC²) / 2 * AB * BC = (196 + 256 – 676) / 2 * 14 * 16 = – 224/448 = – 1/2.
Angle ABC = 120 °.
Answer: The larger angle of the triangle is 120 °.