# Law of Cosines

- Author:
- Esther Gruenhut

- Topic:
- Cosine

In the following applets we derive the cosine law
The first applet is applicable in the case is an acute angle, the second for the case is e an obtuse angle, and the last one for the case of a right angle.

## Acute angle

After scrolling the scroll bar, and unfolding the construction,
use the intersecting chord theorem to obtain:
and therefore:
.

## Obtuse angle

After scrolling the scroll bar, and unfolding the construction,
use the intersecting secant theorem to obtain:
and therefore:
which is equivalent to
.

## Right angle (Pythagorean theorem)

After scrolling the scroll bar, and unfolding the construction,
use the tangent-secant theorem to obtain:
and therefore: