An Obtuse Triangle is defined by having exactly one angle greater than 90 degrees. The Obtuse Triangle Calculator specializes in identifying and solving these “wide” triangles. It takes your partial inputs and computes the full geometry, confirming whether the resulting shape fits the obtuse classification.
Features
Obtuse Detection: Validates that one angle exceeds 90°.
Flexible Inputs: Solves from 3 sides (SSS), 2 sides & angle (SAS), or 2 angles & side (ASA).
Full Dimensions: Calculates the long side opposite the obtuse angle and the two acute angles.
Visual Check: The diagram clearly shows the “stretched” nature of obtuse triangles.
How to Use This Calculator
Select Mode: Choose how you want to define the triangle.
Input: Enter values. For SSS, identifying the longest side is crucial.
Calculate: Process the inputs to find all angles.
Validation: Read the result note to see if it is truly obtuse.
Formulas
The calculator uses the following mathematical principles:
Pythagorean Inequality (Obtuse): $$ c^2 > a^2 + b^2 $$ (where c is the side opposite the obtuse angle).
Law of Cosines: Essential for finding the obtuse angle from sides. $$ \cos C < 0 $$ for angles > 90°.
Angle Sum: $$ A + B + C = 180^\circ $$
Practical Applications
Roofing: Calculating slopes for low-pitch shed roofs.
Landscaping: Planning corner garden beds that are not square.
Mechanism Design: Analyzing linkage positions where arms extend past 90 degrees.
Tips for Success
Only One: A triangle can have at most one obtuse angle.
Longest Side: The side opposite the obtuse angle is always the longest side of the triangle.
Negative Cosine: Remember that the cosine of an obtuse angle is negative, which the calculator handles automatically.
Frequently Asked Questions (FAQ)
Can an obtuse triangle be isosceles?
Yes, if the two acute angles are equal (e.g., 120°, 30°, 30°).
What happens if I enter impossible sides?
The calculator will alert you if the sides do not form a closed triangle (Triangle Inequality).
Final Words
Don’t get bent out of shape by wide angles. The Obtuse Triangle Calculator makes it easy to work with these broad geometries, providing immediate answers and validation.
