SOHCAHTOA Calculator

Category: Geometry
- June 01, 2025
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Solve right triangles using the fundamental trigonometric ratios. SOH-CAH-TOA helps you find missing sides and angles using Sine, Cosine, and Tangent relationships in right triangles.

Triangle Setup

Known Values

Adjacent (b) Opposite (a) Hypotenuse (c) θ 90°
°
The angle opposite to side 'a'
°
The angle opposite to side 'b'
units
Side opposite to angle θ
units
Side adjacent to angle θ
units
Longest side, opposite to 90° angle

Display Options

SOHCAHTOA - Trigonometric Ratios

SOHCAHTOA is a mnemonic device to remember the three basic trigonometric ratios in a right triangle. Each letter represents a ratio relationship between the sides of a right triangle.

The SOHCAHTOA Breakdown
  • SOH: Sine = Opposite / Hypotenuse
  • CAH: Cosine = Adjacent / Hypotenuse
  • TOA: Tangent = Opposite / Adjacent
When to Use Each Ratio
  • Sine (sin): When you know the opposite side and hypotenuse, or need to find one of them
  • Cosine (cos): When you know the adjacent side and hypotenuse, or need to find one of them
  • Tangent (tan): When you know the opposite and adjacent sides, or need to find one of them
Inverse Trigonometric Functions
  • arcsin (sin⁻¹): Find the angle when you know the sine ratio
  • arccos (cos⁻¹): Find the angle when you know the cosine ratio
  • arctan (tan⁻¹): Find the angle when you know the tangent ratio
Right Triangle Properties
  • One angle is always 90° (right angle)
  • The sum of all angles is 180°
  • The two acute angles are complementary (sum to 90°)
  • The hypotenuse is always the longest side
  • Pythagorean theorem: a² + b² = c²
Problem-Solving Strategy
  1. Draw and label the triangle with known information
  2. Identify which side is opposite, adjacent, and hypotenuse relative to the given angle
  3. Choose the appropriate trigonometric ratio based on known and unknown values
  4. Set up the equation and solve
  5. Check your answer using the Pythagorean theorem or other relationships

Disclaimer: This calculator provides solutions for right triangles using basic trigonometric principles. Results are calculated using standard mathematical functions and should be verified for critical applications. Always check that your triangle satisfies the properties of a right triangle (Pythagorean theorem, angle sum = 180°).

What Is the SOHCAHTOA Calculator?

The SOHCAHTOA Calculator is an interactive tool that helps you solve right triangles quickly and accurately. It uses the core trigonometric ratios—Sine, Cosine, and Tangent—to find unknown sides or angles in a right triangle based on the information you already have.

Whether you're trying to calculate triangle dimensions for school, construction, or design, this calculator offers a straightforward solution. It's ideal for anyone needing a reliable triangle Geometry helper or right triangle solver.

Trigonometric Formulas Used

  • SOH: Sine (sin) = Opposite / Hypotenuse
  • CAH: Cosine (cos) = Adjacent / Hypotenuse
  • TOA: Tangent (tan) = Opposite / Adjacent
  • Pythagorean Theorem: a² + b² = c²

How to Use the Calculator

Follow these simple steps to solve right triangles:

  • Select what you want to find: a missing side, a missing angle, or solve the complete triangle.
  • Choose your angle unit: degrees (°) or radians (rad).
  • Enter the known values such as angles or side lengths.
  • Click "Solve Triangle" to get results instantly.
  • Optionally, enable or disable step-by-step solutions, formula displays, and triangle property checks.

What Can You Calculate?

This calculator can be used to:

  • Find missing sides using trigonometric ratios or the Pythagorean Theorem.
  • Determine unknown angles using inverse trigonometric functions.
  • Calculate triangle area and perimeter.
  • Verify triangle properties including angle sum and side relationships.

It's a reliable triangle side and angle tool, perfect for anyone needing to calculate triangle properties or use a hypotenuse finder.

Why Use This Tool?

This right angle math tool simplifies the process of solving triangle problems. Instead of doing the math manually, it uses tested formulas to deliver instant, precise results. Whether you're a student, teacher, engineer, or DIY builder, it serves as a dependable triangle dimension finder and angle and side calculator.

Common Use Cases

  • Education: Learn and apply trigonometry concepts in real time.
  • Engineering: Ensure accurate triangle measurements in designs.
  • Construction: Calculate triangle side lengths and angles on site.
  • Everyday Math: Use it as a quick triangle solver for homework or projects.

Frequently Asked Questions

Can this tool solve all right triangles?

Yes, as long as you provide at least two known values (one of them being a side), the calculator can solve the rest of the triangle using trigonometric principles and the Pythagorean theorem.

Do I need to know all the sides or angles?

No. Entering two values—like one angle and one side—is enough to calculate the rest.

What's the difference between degrees and radians?

Degrees (°) and radians (rad) are two units for measuring angles. The tool supports both, and you can switch based on your preference or curriculum.

Is this calculator the same as a Pythagorean theorem tool?

It includes Pythagorean calculations but offers much more. It's both a Pythagorean theorem solver and a complete Right Triangle Calculator that handles angles too.

What are the required inputs?

You need at least two values—angles or sides. For example, one side and one angle, or two sides.

Summary

The SOHCAHTOA Calculator is a powerful yet simple triangle geometry solver. It helps users solve triangle measurements, apply trigonometric ratios, and verify triangle properties effortlessly. Whether you're using it as a right triangle formula assistant or a triangle area tool, it delivers accurate and educational results every time.