Base of a Triangle Calculator
Solve for the missing base of any triangle using two convenient methods: enter the area and height, or enter two sides and the angle between them and apply the law of cosines.
Method
base = 2 × Area ÷ height
Formula
Substitute
Result
- 1
Double the area
2 × 60 = 120 - 2
Divide by height
120 ÷ 10 = 12
How does this calculator work?
To find a triangle base: if area and height are known, base = 2 × Area ÷ height. If two sides (a, b) and the included angle (C) are known, use the law of cosines: c = √(a² + b² − 2ab·cos C). Both formulas work for any triangle — right, acute or obtuse.
Formula
How this is calculated
Every triangle has a base and a corresponding height (altitude) perpendicular to that base. The area formula Area = ½ × base × height can be rearranged to isolate the base: base = 2 × Area ÷ height. This method works for any triangle — right, acute or obtuse — as long as you know its area and the altitude to the chosen base.
When two sides and the angle between them are known, the Law of Cosines gives the opposite side directly: c² = a² + b² − 2ab·cos(C), so c = √(a² + b² − 2ab·cos C). When C = 90° the cosine term vanishes and this reduces to the Pythagorean theorem. The angle must be strictly between 0° and 180°. If C is obtuse, cos(C) is negative and the formula still works — the base is longer than either of the two sides.
Once the base is known, the full triangle is determined. For the cosine-method result, the triangle area is recovered by Heron's formula using all three sides (a, b, c). The step-by-step panel shows each arithmetic step so you can verify the calculation or adapt it for manual working.
Frequently asked questions
You also need the corresponding height. With area and height both known, use base = 2 × Area ÷ height. If you only know the area and no other measurement, the base is not uniquely determined — infinitely many triangles share the same area.
Yes — when C = 90°, cos(90°) = 0, so the formula reduces to c² = a² + b², which is just Pythagoras's theorem. The law of cosines is the general form that covers right, acute and obtuse triangles.
Both methods still apply. For an equilateral triangle with side a, use the cosine method with b = a and C = 60° to get c = a (confirming all sides equal). For an isosceles triangle, apply whichever method suits the known values.
TG we-Calculate Editorial Team. (2026). Base of a Triangle Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/base-of-a-triangle-calculator
TG we-Calculate Editorial Team. "Base of a Triangle Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/base-of-a-triangle-calculator.
TG we-Calculate Editorial Team, "Base of a Triangle Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/base-of-a-triangle-calculator
@misc{wecalculate_base_of_a_triangle_calculator, title = {Base of a Triangle Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/base-of-a-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?