The hypotenuse of a right-angled triangle is 12 cm, and one of the acute angles is 60 degrees. Find the area of this triangle.

Given:
ABC – right triangle;
angle A = 60 degrees;
AB – hypotenuse;
AB = 12 centimeters;
Find Savs -?
Decision:
1) Consider a right-angled triangle ABC. Angle B = 180 – angle A – angle C, angle B = 180 – 60 – 90,
angle B = 30 degrees.
2) The leg opposite to an angle of 30 degrees is equal to half the hypotenuse. Consequently
AC = 1/2 * AB;
AC = 1/2 * 12;
AC = (1 * 12) / 2;
AC = 6 centimeters;
3) By the Pythagorean theorem, CB ^ 2 = AB ^ 2 – CA ^ 2;
СВ ^ 2 = 144 – 36;
CB ^ 2 = 108;
CB = 6√3 centimeters;
4) Savs = 1/2 * AC * СВ;
Sav = 1/2 * 6 * 6√3;
Sav = 18√3 square centimeters.
Answer: 18√3 square centimeters.