Acute Triangle Calculator
Analyze triangle properties and determine if a triangle is acute, right, or obtuse
Triangle Analysis
Enter Three Side Lengths
Triangle Analysis Results
Enter valid triangle measurements
Make sure the values form a valid triangle
Example Triangle Classifications
Acute Triangle: (3, 4, 4)
Test: 3² + 4² = 9 + 16 = 25 > 4² = 16 ✓
Result: Acute isosceles triangle
Angles: All angles are less than 90°
Right Triangle: (3, 4, 5)
Test: 3² + 4² = 9 + 16 = 25 = 5² = 25
Result: Right scalene triangle
Angles: One angle equals exactly 90°
Obtuse Triangle: (2, 3, 4)
Test: 2² + 3² = 4 + 9 = 13 < 4² = 16
Result: Obtuse scalene triangle
Angles: One angle is greater than 90°
Triangle Classifications
Acute Triangle
All angles < 90°
a² + b² > c²
Right Triangle
One angle = 90°
a² + b² = c²
Obtuse Triangle
One angle > 90°
a² + b² < c²
Quick Reference
Law of Cosines: c² = a² + b² - 2ab cos(C)
Triangle inequality: a + b > c
Angle sum: α + β + γ = 180°
Heron's formula for area
Understanding Acute Triangles
What is an Acute Triangle?
An acute triangle is a triangle where all three interior angles are acute angles, meaning each angle measures less than 90 degrees (π/2 radians). This is in contrast to right triangles (one 90° angle) and obtuse triangles (one angle > 90°).
Law of Cosines Test
To determine if a triangle is acute using side lengths, we use the law of cosines test: For the longest side c and shorter sides a and b, if a² + b² > c², the triangle is acute.
Types by Side Length
- Equilateral: All sides equal (always acute)
- Isosceles: Two sides equal
- Scalene: All sides different
Key Formulas
Law of Cosines: c² = a² + b² - 2ab cos(C)
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Area (Heron's): A = √[s(s-a)(s-b)(s-c)]
where s = (a+b+c)/2
Applications
- •Architecture and structural design
- •Navigation and surveying
- •Computer graphics and game development
- •Physics and engineering calculations