An Acute Triangle is one where *every* internal angle is less than 90 degrees. The Acute Triangle Calculator is designed to verify and solve these specific shapes. Whether you have three sides (SSS) or other combinations, this tool ensures your triangle is truly acute while calculating all its properties.
Features
Acute Verification: Automatically checks if any resulting angle is >= 90° and warns you if the triangle is not Acute.
Multi-Mode Solver: Supports SSS, SAS, and ASA inputs.
Area & Perimeter: Instantly provides the total area using Heron’s formula or trigonometric methods.
Dynamic Visualization: Draws the shape so you can visually confirm the ‘sharpness’ of the angles.
How to Use This Calculator
Choose Mode: frequent use is SSS to check if lengths form an acute shape.
Enter Data: Input your values (e.g., Sides 5, 6, 7).
Compute: Click Calculate.
Check Warnings: Look for the message confirming if the triangle is Acute, Right, or Obtuse.
Formulas
The calculator uses the following mathematical principles:
Pythagorean Inequality: For Acute triangles, $$ a^2 + b^2 > c^2 $$ for all sides (where c is the longest side).
Law of Cosines: Used to find angles from sides. $$ \cos C = (a^2+b^2-c^2)/2ab $$
Heron’s Formula: Area = $$ \sqrt{s(s-a)(s-b)(s-c)} $$
Practical Applications
Architecture: Designing A-frame structures or trusses where sharp angles are required.
Design: Creating logos or patterns relying on equilateral or acute isosceles shapes.
Structural Stability: Acute triangles are often more rigid in truss networks.
Tips for Success
Definition: Remember, even if two angles are acute, if the third is 90° or more, it is NOT an acute triangle.
Equilateral: All equilateral triangles are acute (all angles = 60°).
Input Check: In SSS mode, the sum of any two sides must exceed the third.
Frequently Asked Questions (FAQ)
What if one angle is exactly 90 degrees?
Then it is a Right Triangle, not an Acute Triangle. This calculator will flag that.
Can I solve for just the area?
Yes, just enter the sides or angles defining the shape, and the area is part of the standard output.
Final Words
Precision is key in geometry. The Acute Triangle Calculator helps you define, verify, and solve triangles where sharpness matters, ensuring every angle stays under the limit.
