Right Triangle Angle Calculator 3 Sides

Angle Calculation Formula:

\[ \theta = \arccos\left(\frac{leg1^2 + hyp^2 - leg2^2}{2 \times leg1 \times hyp}\right) \]

Angle θ (degrees):

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1. What is a Right Triangle Angle Calculator?

Definition: This calculator computes an angle in a right triangle when all three side lengths are known.

Purpose: It helps students, engineers, and construction professionals determine angles in right triangles without direct measurement.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

\[ \theta = \arccos\left(\frac{leg1^2 + hyp^2 - leg2^2}{2 \times leg1 \times hyp}\right) \]

Where:

\( \theta \) — Angle opposite Leg 2 (degrees)
\( leg1 \) — First leg length (meters)
\( hyp \) — Hypotenuse length (meters)
\( leg2 \) — Second leg length (meters)

Explanation: The formula calculates the angle between Leg 1 and the Hypotenuse using the relationship between all three sides.

3. Importance of Angle Calculation

Details: Accurate angle calculation is essential for construction, engineering design, navigation, and various scientific applications.

4. Using the Calculator

Tips: Enter all three side lengths in meters. The hypotenuse should be the longest side. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does the calculator work for non-right triangles?
A: While the formula works for any triangle, this calculator assumes a right triangle configuration.

Q2: What units should I use?
A: The calculator uses meters, but any consistent unit will work (cm, inches, feet, etc.).

Q3: How accurate are the results?
A: Results are mathematically precise based on input values, displayed to 2 decimal places.

Q4: What if I get an error?
A: Ensure your inputs form a valid right triangle (hypotenuse² = leg1² + leg2² within floating-point precision).

Q5: Can I calculate the other angles?
A: The remaining angle can be found by subtracting from 90° (since it's a right triangle).