1. What is a Right Triangle?

A right triangle is a triangle with one 90-degree angle. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs. This calculator solves for the unknown angle and hypotenuse when given both legs.

2. How Does the Calculator Work?

The calculator uses these right triangle formulas:

Where:

• \( \theta \) — Angle opposite side a (in degrees)
• \( \text{hyp} \) — Hypotenuse length
• \( a \) — Length of side opposite angle θ
• \( b \) — Length of adjacent side

Explanation: The arctangent function calculates the angle from the ratio of the opposite to adjacent sides, while the Pythagorean theorem calculates the hypotenuse.

3. Importance of Right Triangle Calculations

Details: Right triangle calculations are fundamental in trigonometry, physics, engineering, architecture, and navigation. They're used to determine distances, angles, and relationships between components in many practical applications.

4. Using the Calculator

Tips: Enter the lengths of both legs (a and b) in any consistent units. The calculator will output the angle θ in degrees and the hypotenuse in the same units as the legs.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the hypotenuse and one leg?
A: You can modify the formulas to solve for the missing leg using \( a = \sqrt{\text{hyp}^2 - b^2} \) and then find the angle.

Q2: Can I use this for non-right triangles?
A: No, these formulas only work for right triangles. For other triangles, you would need the Law of Sines or Cosines.

Q3: How precise are the results?
A: Results are rounded to 2 decimal places. For most practical applications, this provides sufficient precision.

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

Q5: Can I calculate area with this?
A: While this calculator doesn't directly compute area, you can easily find it with \( \text{Area} = \frac{1}{2} \times a \times b \).