How to Use the SOHCAHTOA Calculator

Welcome to our easy-to-use SOHCAHTOA Calculator! Follow these steps to solve your triangle problems quickly and accurately:

1. Choose Your Triangle Type: Start by selecting “Right Triangle” or “Non-Right Triangle” from the “Triangle Type” dropdown.
   • For right triangles, you’ll need just 2 values.
   • For non-right triangles, provide at least 3 values (a third field will appear).
2. Enter Your Values: Input the known measurements into the fields:
   • Side a, Side b, Side c: These are the lengths of the triangle’s sides.
   • Angle α, Angle β, Angle γ: These are the angles in your triangle (γ appears for non-right triangles).
   Hover over the labels to see helpful tips about each field!
3. Select Angle Unit: Choose “Degrees” or “Radians” from the “Angle Unit” dropdown to match your angle measurements.
4. Calculate: Click the blue “Calculate Now” button. The tool will process your inputs and display the results instantly.
5. Review Results: Check the “Results” section for all calculated values (sides, angles, height, area, etc.), followed by a step-by-step breakdown in the “Steps” section.

Tips:

• Ensure your values make sense (e.g., angles in a right triangle must add up to 90°, or 180° for non-right).
• If you see an error, double-check your inputs and try again.
• Use positive numbers only—negative values aren’t valid for triangle sides or angles.

That’s it! Whether you’re tackling homework or exploring geometry, this tool has you covered.

Formulas

Our calculator uses these key mathematical formulas to solve your triangles. Here’s what powers the magic:

For Right Triangles

• SOH (Sine): \(\sin(\alpha) = \frac{\text{Side a (Opposite)}}{\text{Side c (Hypotenuse)}}\)
• CAH (Cosine): \(\cos(\alpha) = \frac{\text{Side b (Adjacent)}}{\text{Side c (Hypotenuse)}}\)
• TOA (Tangent): \(\tan(\alpha) = \frac{\text{Side a (Opposite)}}{\text{Side b (Adjacent)}}\)
• Pythagorean Theorem: \(c = \sqrt{a^2 + b^2}\), where \(c\) is the hypotenuse.
• Height (h): \(h = \frac{a \cdot b}{c}\), the altitude from the right angle to the hypotenuse.
• Area: \(\text{Area} = \