In a triangle ABC, AC = 40 cm, BC = 4 cm. Find AB.

Hello!

There are no sufficient data to find AB. By the triangle inequality it can be of any length between 40 cm - 4 cm = 36 cm and 40 cm + 4 cm = 44 cm (excluding the endpoints). Please look at the picture.

If we would know the measure of the angle ACB (denote it as ), then we could find AB by the law of cosines:

Some other data...

Hello!

There are no sufficient data to find AB. By the triangle inequality it can be of any length between 40 cm - 4 cm = 36 cm and 40 cm + 4 cm = 44 cm (excluding the endpoints). Please look at the picture.

If we would know the measure of the angle ACB (denote it as ), then we could find AB by the law of cosines:

Some other data may also help us to find AB.