In a right-angled triangle ABC, the outside angle at apex A is 120 °. Leg AC = 17. Find the hypotenuse AB.

1. It is known that the sum of adjacent angles is 180 *.

2. If the external angle at the vertex A of the triangle ABC is 120 *, then the angle A as adjacent to the external angle is 180 * – 120 * = 60 *.

3. By definition, the cosine of an acute angle in a right-angled triangle is the ratio of the adjacent leg to the hypotenuse.

So in the triangle ABC

AC: AB = cos of angle A.

According to the condition of the problem, the leg AC = 17, according to the table cos 60 * = 1/2, you can find the hypotenuse AB.

AB = AC: cos 60 * = 17: 1/2 = 34.

Answer: The hypotenuse of triangle ABC is 34 units.