Hinge Theorem Calculator

Calculate the Length of the Third Side





Formula

The formula to calculate the length of the third side using the Hinge Theorem is:

\[ c = \sqrt{a^2 + b^2 - 2ab \cdot \cos(C)} \]

Where:

What is the Hinge Theorem?

The Hinge Theorem, also known as the Law of Cosines, is a principle in geometry that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is used to calculate the length of an unknown side of a triangle when two sides and the included angle are known. This theorem is particularly useful in various fields such as engineering, architecture, and navigation.

Example Calculation

Let's assume the following values:

Using the formula to calculate the length of the third side (c):

\[ c = \sqrt{5^2 + 7^2 - 2 \cdot 5 \cdot 7 \cdot \cos(60^\circ)} \approx 6.24 \text{ units} \]

The length of the third side is approximately 6.24 units.