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: