Shape of a Triangle

The shape of triangle can be determined by expressing the angles , , and in terms of the side lengths , , and .

1. Using the Law of Sines

  1. If the circumradius of triangle is denoted by , then:
  2. The ratio of the sides is:

Explanation:

From the Law of Sines, , we get:
Thus, .

2. Using the Law of Cosines

Explanation:

From the Law of Cosines, , we get:
Similarly, we can derive: