**Q: What is a right triangle?**

A: A right triangle is a type of triangle that has one angle measuring 90 degrees. It is characterized by having one side called the hypotenuse, which is the longest side and is opposite the right angle. The other two sides are called the legs of the right triangle.

**Q: What can the Right Triangle Calculator solve?**

A: The Right Triangle Calculator can solve various properties of a right triangle, including the lengths of the sides and the measures of the angles. It uses the Pythagorean theorem to calculate the unknown side lengths and the trigonometric ratios to determine the angles. Additionally, it can calculate the area and perimeter of the right triangle.

**Q: How does the calculator work?**

A: The calculator uses the Pythagorean theorem (a^2 + b^2 = c^2) to find the lengths of the sides of the right triangle. It also utilizes the trigonometric functions (sine, cosine, and tangent) to determine the angles. By providing the necessary inputs, such as side lengths or angle measures, the calculator can solve for the unknown properties of the right triangle.

**Q: What are Pythagorean triangles?**

A: Pythagorean triangles, also known as Pythagorean triples, are right triangles where the lengths of all three sides are integers. These triangles satisfy the Pythagorean theorem, and they have been studied for centuries. Examples of Pythagorean triples include 3, 4, 5 and 5, 12, 13.

**Q: How is the area and perimeter of a right triangle calculated?**

A: The area of a right triangle is calculated using the formula A = (1/2) * base * height, where the base and height are the lengths of the two legs of the right triangle. The perimeter of a right triangle is determined by adding the lengths of all three sides of the triangle.

**Q: What are the Greek symbols α and β used for in the calculator?**

A: In the Right Triangle Calculator, the Greek symbols α (alpha) and β (beta) are used to represent the unknown angle measures of the right triangle. The angles are typically denoted by the corresponding capitalized letter (A, B, C), but in the calculator, α and β are used for convenience.