In a right-angled triangle ABC with a right angle C, the outer angle at the vertex A is equal to 120 degrees

In a right-angled triangle ABC with a right angle C, the outer angle at the vertex A is equal to 120 degrees AC + AB = 18cm. Find AB and AC.

1. Subtracting the external angle, equal to 120º, from the value of the expanded angle, we calculate

inner corner of the triangle at the vertex A:

180 – 120 = 60º.

2. We calculate the value of the angle ABC:

180 – 90 – 60 = 30º.

3. Using the theorem that the leg opposite an angle equal to 30º is 1/2

the hypotenuse of the triangle, we find the AC leg:

AC = AB / 2;

4. Substitute AC = AB / 2 into the expression AC + AB = 18:

AB / 2 + AB = 18;

AB = 18: 1.5 = 12 cm;

AC = 18 – 12 = 6 cm.

Answer: AB length is 12 cm, AC length is 6 cm.