One of the acute angles of the triangle is 60 degrees. The sum of the smaller leg

One of the acute angles of the triangle is 60 degrees. The sum of the smaller leg and the hypotenuse = 3.6 dm. Find the length of the smaller leg and hypotenuse.

In a right-angled triangle, the legs form a right angle (90 °), and the side opposite to the right angle is called the hypotenuse. If there is an angle of 60 ° in a right-angled triangle, then the hypotenuse is equal to the two smaller legs of the triangle. Let us denote the smaller leg by the letter a, the hypotenuse by the letter c:

a + c = 3.6 dm;

Let us express the hypotenuse through the smaller leg:

c = 2a;

a + 2a = 3.6 dm;

3a = 3.6 dm;

a = 3.6 / 3 = 1.2 dm – the smaller leg of the triangle;

c = 2a = 1.2 * 2 = 2.4 dm – the hypotenuse of the triangle.

Answer: 1.2 dm; 2.4 dm.