Angle Calculator Right Angled Triangle

Angle Formula:

\[ \theta = \arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right) \]

Angle θ (degrees):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is an Angle Calculator for Right-Angled Triangles?

Definition: This calculator determines an angle in a right-angled triangle when given the lengths of the opposite and adjacent sides.

Purpose: It helps students, engineers, and construction professionals quickly calculate angles without manual trigonometry.

2. How Does the Calculator Work?

The calculator uses the arctangent function:

\[ \theta = \arctan\left(\frac{\text{opposite}}{\text{adjacent}}\right) \]

Where:

\( \theta \) — Angle in degrees
opposite — Length of side opposite to the angle
adjacent — Length of side adjacent to the angle

Explanation: The ratio of opposite to adjacent sides gives the tangent of the angle, and the arctangent function converts this ratio back to the angle.

3. Importance of Angle Calculation

Details: Accurate angle calculation is crucial in construction, engineering, navigation, and various scientific applications involving right triangles.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides in meters (or any consistent unit). Both values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the hypotenuse instead?
A: Use arcsine (opposite/hypotenuse) or arccosine (adjacent/hypotenuse) instead of arctangent.

Q2: Does this work for non-right triangles?
A: No, this calculator is specifically for right-angled triangles. Use the Law of Cosines for other triangles.

Q3: What's the range of possible angles?
A: The calculator returns angles between 0° and 90° (exclusive) for valid inputs.

Q4: Can I use different units?
A: Yes, as long as both sides use the same unit (meters, feet, etc.), the angle result will be correct.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise, though displayed results are rounded to 2 decimal places.