1. What is a Right Triangle?

A right triangle is a triangle with one angle exactly 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs. The relationship between these sides is described by the Pythagorean theorem.

2. How Does the Calculator Work?

The calculator uses trigonometric functions to calculate the legs of a right triangle:

Where:

• \( a \) — First leg (opposite to angle θ)
• \( b \) — Second leg (adjacent to angle θ)
• hypotenuse — Longest side of the right triangle
• θ — Angle between hypotenuse and leg b (in degrees)

Explanation: The sine function gives the ratio of the opposite side to the hypotenuse, while the cosine gives the ratio of the adjacent side to the hypotenuse.

3. Importance of Right Triangle Calculations

Details: Right triangle calculations are fundamental in geometry, physics, engineering, and many practical applications like construction and navigation.

4. Using the Calculator

Tips: Enter the hypotenuse length and one angle (θ) between 0 and 90 degrees. The calculator will compute both legs of the triangle.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the legs but not the hypotenuse?
A: You can use the Pythagorean theorem: hypotenuse = √(a² + b²).

Q2: Can I use radians instead of degrees?
A: This calculator uses degrees, but the formulas work with radians if you convert accordingly (180° = π radians).

Q3: What's the range of valid angles?
A: For a right triangle, the angle θ must be between 0 and 90 degrees (non-inclusive).

Q4: What if my angle is 0° or 90°?
A: At 0°, leg a becomes 0 and leg b equals the hypotenuse. At 90°, leg b becomes 0 and leg a equals the hypotenuse.

Q5: Can this be used for non-right triangles?
A: No, these formulas are specific to right triangles. For other triangles, you would use the Law of Sines or Cosines.