Enter the lengths of two sides and the included angle of a triangle into the calculator to determine the length of the third side using the Hinge Theorem.
Hinge Theorem Formula
The following formula is used to calculate the length of the third side of a triangle based on the Hinge Theorem.
c = √(a^2 + b^2 - 2ab * cos(C))
Variables:
- c is the length of the third side (units)
- a is the length of side A (units)
- b is the length of side B (units)
- C is the included angle between sides A and B (degrees)
To calculate the length of the third side (c), use the Law of Cosines with the given lengths of sides A and B and the included angle C.
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.
How to Calculate the Length of the Third Side?
The following steps outline how to calculate the length of the third side of a triangle using the Hinge Theorem.
- First, determine the lengths of sides A and B of the triangle.
- Next, determine the included angle C between sides A and B in degrees.
- Use the formula c = √(a^2 + b^2 – 2ab * cos(C)) to calculate the length of the third side (c).
- Convert angle C from degrees to radians by multiplying it by π/180.
- Finally, calculate the length of the third side (c) using the Law of Cosines.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Length of side A (a) = 5 units
Length of side B (b) = 7 units
Included angle C = 60 degrees
