One of the acute angles of a right-angled triangle is 60 °. The sum of the lesser leg and

One of the acute angles of a right-angled triangle is 60 °. The sum of the lesser leg and the hypotenuse is 2.64 cm. Find the length of the hypotenuse of the triangle.

A right-angled triangle is a triangle in which one corner is a straight line, that is, it is equal to 90 degrees. The side opposite the right angle is the hypotenuse, and the sides opposite the sharp corners are the legs.

In a right-angled triangle, the acute angles add up to 90 degrees. If one acute angle is 60 °, then the second acute angle is 90 ° – 60 ° = 30 °.

The smaller leg lies opposite the smaller acute angle, and the larger leg is opposite the larger acute angle. This means that our smaller leg lies opposite an angle of 30 °. The leg opposite the 30 ° angle is half the hypotenuse.

Let the smaller leg be x cm, then the hypotenuse is 2x cm.By the condition of the problem, it is known that the sum of the smaller leg and the hypotenuse is (x + 2x) cm or 2.64 cm.Let’s make an equation and solve it.

x + 2x = 2.64;

3x = 2.64;

x = 2.64: 3;

x = 0.88 (cm) – leg;

2x = 0.88 * 2 = 1.76 (cm) – hypotenuse.

Answer. 1.76 cm.