One of the corners of a right-angled triangle is 60 degrees, and the sum of the hypotenuse

One of the corners of a right-angled triangle is 60 degrees, and the sum of the hypotenuse and the smaller leg is 42 cm. Find the hypotenuse.

ABC – right-angled triangle, angle B = 90 degrees, angle C = 60 degrees, AB and BC – legs, AC – hypotenuse.
angle A + angle B + angle C = 180 degrees (according to the theorem on the sum of the angles of a triangle);
angle A + 90 + 60 = 180;
angle A = 180 – 150;
angle A = 30 degrees.
Opposite the angle of 30 degrees lies the leg, which is equal to half the hypotenuse, then:
BC = AC / 2.
The sum of the hypotenuse and the smaller leg is 42. The smaller leg in ABC is the leg BC, because the smaller angle A rests on it, therefore:
AC + BC = 42 cm.
We get the system of equations:
BC = AC / 2;
AC + BC = 42.
Substitute the first expression in the second instead of BC and find the length of the AC hypotenuse:
AC + AC / 2 = 42;
(2AC + AC) / 2 = 42;
3AC / 2 = 42;
3AC = 84;
AC = 84/3;
AC = 28 cm.
Answer: AC = 28 cm.