Quick start
- Enter sides a, b and c in the same unit.
- Read the area, perimeter and angles.
- Check the type: equilateral, isosceles or scalene, and acute, right or obtuse.
Area with Heron's formula
First find the semi-perimeter, s = (a + b + c) ÷ 2. Then area = √(s(s − a)(s − b)(s − c)). For sides 7, 8 and 9: s = 12, so the area is √(12 × 5 × 4 × 3) = √720 ≈ 26.83.
Angles with the law of cosines
cos A = (b² + c² − a²) ÷ 2bc, and the same pattern gives B and C. For the 7-8-9 triangle, the angle opposite the side of 7 is about 48.19°. The three angles always total 180°.
Is it a real triangle?
Any two sides together must be longer than the third. Sides 2, 3 and 6 fail, because 2 + 3 is less than 6. The calculator checks this before doing anything else.
Acute, right or obtuse?
Compare the square of the longest side with the sum of the squares of the other two. Equal means a right angle. Smaller means all angles are acute. Bigger means one angle is obtuse.
Common questions
Can I enter two sides and an angle?
This tool works from three sides. For a right triangle with two known sides, use the Pythagorean Theorem Calculator.
How are the heights found?
Each height is 2 × area ÷ the side it stands on.
What units does the area use?
The square of the unit you used for the sides.