One of the outer corners of the triangle is 120 degrees. The sum of the hypotenuse and

One of the outer corners of the triangle is 120 degrees. The sum of the hypotenuse and the smaller leg is 15 cm. Find the sides of the triangle.

In a right-angled triangle, the outer angle is 120 °, so the inner angle is 60 °.

The second acute angle will be 90 ° – 60 ° = 30 °.

Let’s denote the hypotenuse for x, then the leg, lying opposite an angle of 30 ° is equal to half of the hypotenuse, that is, x / 2.

x + x / 2 = 15;

3x = 30;

x = 10.

10cm – hypotenuse, smaller leg – 5cm.

Let’s find the second leg according to the Pythagorean theorem: 10^2 = 5^2 + y^2; where y is the second leg.

y^2 = 100 – 25;

y^2 = 75;

y = √75 = 5√3.

Answer: 10cm, 5cm, 5√3cm.