Right Triangle Calculator

Right Triangle Formulas:

\[ a^2 + b^2 = c^2 \] \[ \sin(\theta) = \frac{opposite}{hypotenuse} \] \[ \cos(\theta) = \frac{adjacent}{hypotenuse} \] \[ \tan(\theta) = \frac{opposite}{adjacent} \]

Side A:

Side B:

Side C (Hypotenuse):

Angle A:

degrees

Angle B:

degrees

Side A:

Side B:

Side C (Hypotenuse):

Angle A:

Angle B:

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1. What is a Right Triangle?

A right triangle is a triangle in which one angle is exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and it is always the longest side of the triangle.

2. How Does the Calculator Work?

This calculator uses the Pythagorean theorem and trigonometric functions to calculate missing sides and angles of a right triangle. You need to provide at least two known values (sides or angles).

3. Pythagorean Theorem

\[ a^2 + b^2 = c^2 \]

Where:

\( a \) and \( b \) — Legs of the right triangle
\( c \) — Hypotenuse (side opposite the right angle)

4. Trigonometric Functions

For angle θ in a right triangle:

\[ \sin(\theta) = \frac{opposite}{hypotenuse} \] \[ \cos(\theta) = \frac{adjacent}{hypotenuse} \] \[ \tan(\theta) = \frac{opposite}{adjacent} \]

5. Frequently Asked Questions (FAQ)

Q1: What is the minimum information needed to calculate a right triangle?
A: You need at least two known values: either two sides, or one side and one angle (other than the 90° angle).

Q2: Why is the hypotenuse always the longest side?
A: According to the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the other two sides, making it necessarily longer than either leg.

Q3: Can I use this calculator for non-right triangles?
A: No, this calculator is specifically designed for right triangles. For other triangles, you would need different formulas like the Law of Sines or Law of Cosines.

Q4: What units should I use for measurements?
A: You can use any consistent units for sides (meters, centimeters, inches, etc.). Angles should be in degrees.

Q5: How accurate are the calculations?
A: The calculations are mathematically precise based on the inputs provided. Results are rounded to 4 decimal places for readability.