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Right Triangle Sides and Angles Calculator

Right Triangle Formulas:

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

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1. What is a Right Triangle Calculator?

Definition: This calculator computes the hypotenuse and angles of a right triangle based on the lengths of its two legs.

Purpose: It helps students, engineers, and construction professionals solve right triangle problems quickly and accurately.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem and trigonometric functions:

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

Where:

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: Right triangle calculations are fundamental in geometry, construction, navigation, and various engineering applications.

4. Using the Calculator

Tips: Enter the lengths of both legs in meters. All values must be positive numbers. The calculator will compute the hypotenuse and the angle opposite to side b.

5. Frequently Asked Questions (FAQ)

Q1: What units does this calculator use?
A: The calculator uses meters for length inputs and outputs, but you can use any consistent unit of measurement.

Q2: Can I calculate one side if I know the hypotenuse and one leg?
A: This version requires both legs. For other combinations, you would need a different calculator.

Q3: How accurate are the results?
A: Results are accurate to 3 decimal places for lengths and 2 decimal places for angles.

Q4: What if I need the other angle?
A: The other acute angle in a right triangle is always (90° - θ).

Q5: Does this work for non-right triangles?
A: No, this calculator is specifically for right triangles. For other triangles, you would need the Law of Cosines or Law of Sines.

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