Missing Sides of Triangle Calculator

Calculate unknown triangle sides from common givens quickly. Switch methods, inspect steps, and visualize outputs. Save tables, export reports, and study worked examples confidently.

Calculator

Solve method

Unit label

Decimal places

Right triangle inputs

Enter exactly two sides. Side c is the hypotenuse.

Side a

Side b

Side c

SAS inputs

Enter sides b and c with the included angle A.

Side b

Side c

Included angle A (degrees)

Two angles and one side

Enter angles A and B, then choose one known opposite side.

Angle A (degrees)

Angle B (degrees)

Known side label

Known side value

Example Data Table

Method	Input Example	Computed Missing Side(s)	Notes
Right triangle	a = 3, b = 4	c = 5	Classic Pythagorean example.
Right triangle	b = 12, c = 13	a = 5	Hypotenuse must stay largest.
SAS triangle	b = 7, c = 10, A = 30°	a ≈ 5.27	Uses the cosine rule.
Angle-based	A = 40°, B = 65°, a = 8	b ≈ 11.10, c ≈ 9.44	Uses the sine rule.

Formula Used

1) Right triangle method

Use the Pythagorean theorem when the triangle has one right angle.

c = √(a² + b²)

a = √(c² - b²)

b = √(c² - a²)

Here, c is the hypotenuse. It must always be the longest side.

2) SAS method

Use the cosine rule when you know two sides and their included angle.

a² = b² + c² - 2bc cos(A)

This finds the third side directly from two known sides and angle A.

3) Angle-based method

Use the sine rule when you know two angles and one side opposite a known angle.

a / sin(A) = b / sin(B) = c / sin(C)

First find the third angle.

C = 180° - A - B

4) Extra measures

Perimeter adds all side lengths. Semi-perimeter is half the perimeter.

Area for solved triangles can be found with:

Area = 1/2 × b × c × sin(A)

How to Use This Calculator

Choose the solving method that matches your known values.
Enter the triangle measurements in the visible input fields.
Add a unit label if you want labeled output values.
Choose the number of decimal places for the results.
Press calculate to show the solved sides above the form.
Review side lengths, angles, perimeter, semi-perimeter, and area.
Use the CSV or PDF buttons to save the result table.
Inspect the Plotly graph to compare the solved side lengths.

FAQs

1) What does this calculator solve?

It solves missing triangle sides using three common setups: right triangle, SAS, and two-angles-with-one-side input.

2) When should I use the right triangle option?

Use it only when one angle is exactly 90 degrees and you know any two side lengths.

3) What is the hypotenuse?

The hypotenuse is the side opposite the right angle. It is always the longest side in a right triangle.

4) What does SAS mean?

SAS means side-angle-side. You know two sides and the angle between them, so the cosine rule can find the third side.

5) Why must two angles add to less than 180 degrees?

A triangle’s interior angles always total 180 degrees. If two given angles already reach or exceed that, no triangle exists.

6) Does the calculator also return angles?

Yes. After solving the missing side values, it also reports all three triangle angles for easy verification.

7) Can I export the result?

Yes. The result table can be downloaded as CSV or PDF after a successful calculation.

8) What units should I enter?

Use any consistent unit, such as cm, m, inches, or feet. The calculator keeps the same unit across solved sides.