Cosine Rule Calculator
Calculate the unknown side or angle of a triangle using the cosine rule. Enter two sides and the included angle to find the third side, or three sides to find an angle.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator uses the Cosine Rule to solve triangles. It has two modes:
- Find Side (SSA): Given two sides (b, c) and the included angle (A), it calculates the third side (a).
- Find Angle (SSS): Given all three sides (a, b, c), it calculates angle A.
Step-by-step:
- Select the calculation mode from the dropdown.
- Enter the required values (positive numbers). For angles, use degrees between 0 and 180.
- Click Calculate.
- The result (side length or angle in degrees) appears below, along with the formula used.
Note: All sides must be in the same unit (e.g., meters, feet). The calculator does not convert units. If using "Find Angle," ensure the three sides satisfy the triangle inequality (each side less than the sum of the other two) – otherwise an error is shown.
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Frequently Asked Questions
The cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles. It is used to find a side when two sides and the included angle are known, or an angle when three sides are known.
To find a side, enter two sides and the included angle (in degrees). To find an angle, enter all three sides.
Yes, as long as the inputs satisfy the triangle inequality (for SSS) or the angle is between 0 and 180 degrees (for SSA).
