How this calculator works
Perimeter is the distance around the boundary. If one side is unknown, subtract the known sides from the perimeter and check the triangle inequality. With an included angle the law of cosines supplies the missing side. With two angles and their included side, the angle sum and law of sines determine the other sides before addition.
Formula
P=a+b+c; missing c=P-a-b; SAS: c²=a²+b²-2ab cos C; ASA: A=180°-B-C, b=a sin B/sin A, c=a sin C/sin A.
Worked example
Sides 3 cm, 4 cm and 5 cm have perimeter 12 cm. With perimeter 30 m and known sides 8 m and 10 m, the remaining side is 12 m, which satisfies the triangle inequality.
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Frequently asked questions
Can any positive perimeter work with two fixed sides?
No. The recovered side must be positive and lie strictly between the difference and sum of the other two sides.
Is perimeter affected by orientation?
No. Rotating or reflecting a triangle does not change the side lengths or their sum.
Is the angle in SAS between the known sides?
Yes. Here C lies between sides a and b. A different known angle is an SSA problem and may have two solutions.