Right Triangle Angle Calculator

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Right Triangle Angle Calculator

Right triangles are essential in geometry and trigonometry, featuring one 90° angle and two acute angles. Whether you’re a student, engineer, or enthusiast, calculating unknown sides or angles quickly can save time and avoid errors.

Our Right Triangle Angle Calculator allows you to input any two sides of a right triangle and instantly calculates the third side, all angles, area, and perimeter. This interactive tool simplifies solving right triangle problems for homework, design, or practical applications.

How to Use the Right Triangle Angle Calculator

You can enter any two known sides of the right triangle:

  • Side A (Adjacent)
  • Side B (Opposite)
  • Side C (Hypotenuse) (optional)

Once two sides are entered, click Calculate to get:

  • The length of the missing side
  • Angle A (in degrees) opposite side A
  • Angle B (in degrees) opposite side B
  • Angle C (always 90°)
  • Area of the triangle
  • Perimeter of the triangle

If you want to reset the inputs, click Reset.

Example Calculation

Suppose you know:

  • Side A = 3 units
  • Side B = 4 units
  • Side C = unknown

Enter 3 for Side A and 4 for Side B, then hit Calculate.

The tool will calculate:

  • Side C (Hypotenuse) = 5 units (by Pythagoras theorem)
  • Angle A ≈ 53.13°
  • Angle B ≈ 36.87°
  • Area = 6 sq units
  • Perimeter = 12 units

How the Calculator Works (Formulas Used)

  • Pythagorean Theorem: c=a2+b2c = \sqrt{a^2 + b^2}c=a2+b2​ or a=c2−b2,b=c2−a2a = \sqrt{c^2 – b^2}, \quad b = \sqrt{c^2 – a^2}a=c2−b2​,b=c2−a2​
  • Angles: θA=arctan⁡(ba)×180π\theta_A = \arctan\left(\frac{b}{a}\right) \times \frac{180}{\pi}θA​=arctan(ab​)×π180​ θB=90∘−θA\theta_B = 90^\circ – \theta_AθB​=90∘−θA​
  • Area: Area=12×a×b\text{Area} = \frac{1}{2} \times a \times bArea=21​×a×b
  • Perimeter: Perimeter=a+b+c\text{Perimeter} = a + b + cPerimeter=a+b+c

Frequently Asked Questions (FAQs)

1. What if I only know one side?
You need to enter at least two sides for the calculator to work.

2. Can this calculator handle non-right triangles?
No, it only works for right triangles where one angle is 90°.

3. What units should I use?
Any unit of length (meters, feet, inches) can be used as long as they are consistent.

4. Why is Side C called the hypotenuse?
The hypotenuse is the longest side opposite the right angle in a right triangle.

5. Can the calculator detect invalid input?
Yes, it alerts if the hypotenuse is not longer than the other sides.

6. Does it calculate angles in degrees or radians?
This calculator provides angles in degrees.

7. Can I use this for trigonometry homework?
Absolutely, it’s a helpful tool to verify your calculations.

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