The Missing Side of Triangle Calculator is a comprehensive solver that handles multiple geometry scenarios. It integrates the Law of Sines, Law of Cosines, and Pythagorean logic to solve for ‘x’ in Side-Angle-Side (SAS), Angle-Angle-Side (AAS), and Right triangle configurations.
Features
Trigonometry Power: Solves complex oblique triangles using Law of Sines and Cosines.
Scenario Based: Clearly labeled modes for SAS, AAS, and Right Triangles.
Full Working: Shows the substitution of values into the trigonometric formulas.
Canvas Draw: Visualizes the calculated triangle.
How to Use This Calculator
Select Configuration: Choose SAS, AAS, or Right Triangle based on your knowns.
Input Variables: Enter sides and angles (e.g., Side a, Side b, Angle C).
Execute: Click “Find Missing Side” to compute the result.
Learn: Read the generated explanation to understand the trig used.
Formulas
The calculator uses the following mathematical principles:
Law of Cosines (SAS): Used when you have two sides and the angle between them. $$ c = \sqrt{a^2 + b^2 – 2ab \cos(C)} $$
Law of Sines (AAS): Used when you have two angles and a non-included side. $$ \frac{a}{\sin A} = \frac{b}{\sin B} \implies b = \frac{a \cdot \sin B}{\sin A} $$
Pythagorean Theorem: For right triangles. $$ c^2 = a^2 + b^2 $$
Practical Applications
Surveying: Triangulation uses these laws to map distances across obstacles like rivers.
Astronomy: Calculating distances to nearby stars using parallax (triangles).
Machining: programming CNC paths often requires solving for missing lengths based on angular cuts.
Tips for Success
AAS vs ASA: The Law of Sines works for both. If you have ASA, you can find the third angle (180 – A – B) and then use Law of Sines.
Ambiguity: For Law of Sines, ensure you associate the side with the correct opposite angle.
Degrees: This calculator assumes angle inputs are in degrees.
Frequently Asked Questions (FAQ)
What is SAS?
SAS stands for Side-Angle-Side. It means you know two side lengths and the angle contained between them.
Can I solve for an angle with this?
This specific tool is optimized for finding a *side*. Please use our ‘Angle of Triangle Calculator’ if you need to find unknown angles.
Final Words
Stop guessing and start solving. The Missing Side of Triangle Calculator uses the power of trigonometry to fill in the blanks of any triangle geometry problem.
