Right Triangle Side and Angle Calculator

Right Triangle Formulas:

\[ \theta = \arctan(a/b) \] \[ c = \sqrt{a^2 + b^2} \]

Hypotenuse (c):

Angle (θ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Right Triangle Calculation?

Right triangle calculations involve finding missing sides or angles in a triangle with one 90-degree angle. The calculator helps find the hypotenuse and angle θ given the two legs (a and b) of the triangle.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem and trigonometric functions:

\[ c = \sqrt{a^2 + b^2} \] \[ \theta = \arctan\left(\frac{a}{b}\right) \]

Where:

\( a \) — First leg of the right triangle
\( b \) — Second leg of the right triangle
\( c \) — Hypotenuse (longest side)
\( \theta \) — Angle opposite side a

Explanation: The hypotenuse is calculated using the Pythagorean theorem, while the angle is found using the arctangent of the ratio of the two legs.

3. Importance of Right Triangle Calculations

Details: These calculations are fundamental in geometry, physics, engineering, and many practical applications like construction and navigation.

4. Using the Calculator

Tips: Enter the lengths of both legs (a and b) in any consistent units. The angle can be displayed in degrees or radians. Both legs must be positive values.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the hypotenuse and one leg?
A: You can modify the formula to find the missing leg: \( a = \sqrt{c^2 - b^2} \).

Q2: How accurate are the results?
A: Results are mathematically exact (within floating-point precision) for given inputs.

Q3: Can I use this for non-right triangles?
A: No, different formulas (Law of Cosines/Sines) are needed for non-right triangles.

Q4: What units should I use?
A: Any consistent units (cm, m, inches, etc.) can be used as long as both legs are in the same units.

Q5: What's the range for the angle θ?
A: θ will always be between 0 and 90 degrees (0 and π/2 radians) for positive a and b values.