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:
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.
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.
