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 `gamma`), then we could find AB by the law of cosines:

`AB = sqrt(AC^2+BC^2-2*AC*BC*cos(gamma)).`

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 `gamma`), then we could find AB by the law of cosines:

`AB = sqrt(AC^2+BC^2-2*AC*BC*cos(gamma)).`

Some other data may also help us to find AB.