Triangle calculators

Find Missing Side of Triangle Calculator

Calculate a missing side and see which formula applies.

Missing sidesAnglesArea & perimeterStep-by-step formula path

Calculate triangle values

Enter the known values for this triangle case. Results are educational estimates for geometry and measurement problems.

Result

What this calculator does

This page focuses on missing side questions. Use the right-triangle path when a 90° angle is known, or use the SAS path when two sides and the included angle are known.

Right triangleUse a² + b² = c² when the triangle has a 90° angle.
SAS caseUse the law of cosines when two sides and the included angle are known.
With stepsThe result includes the formula path used.
For classroom work, check the required rounding rules and whether angles are in degrees or radians. This page uses degrees.

Which missing side formula should you use?

The phrase “missing side of a triangle” can mean several different problems. The safest approach is to identify the triangle case first, then apply the matching formula.

Known informationFormula pathExample use
Right triangle with two legsc = √(a² + b²)Find the hypotenuse
Right triangle with hypotenuse and one lega = √(c² − b²)Find a missing leg
Two sides and included anglez² = x² + y² − 2xy cos(C)Find the opposite side in a non-right triangle
One side and two anglesLaw of SinesFind the remaining sides after finding the third angle

Step-by-step example: missing side of a right triangle

If the two known legs are 6 and 8, the missing hypotenuse is found with the Pythagorean theorem.

  1. Start with a² + b² = c².
  2. Substitute the known legs: 6² + 8² = c².
  3. Calculate: 36 + 64 = 100.
  4. Take the square root: c = √100 = 10.

So the missing hypotenuse is 10 units.

Step-by-step example: missing side with SAS

If two sides and the included angle are known, the law of cosines is usually the right tool. For sides 7 and 9 with included angle 60°, the missing side z is calculated from z² = 7² + 9² − 2 × 7 × 9 × cos(60°).

This page’s calculator performs that formula and returns the missing side, while the full triangle solver can continue by calculating angles, area, and perimeter.

If the known angle is not between the two known sides, you may have an SSA case. SSA can have one solution, two solutions, or no valid triangle.

Frequently asked questions

Can I find a missing side with only one side?

No. A triangle is not determined by one side alone. You need more information, such as another side, an angle, or a right angle relationship.

Can three sides find a missing side?

If all three sides are already known, there is no missing side. Use the SSS calculator to find angles, area, perimeter, and triangle type.

What if the calculator says no valid triangle?

The side lengths may violate triangle inequality, or the angle-side combination may not describe a possible triangle.

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