1. What is Right Triangle Trigonometry?

Right triangle trigonometry involves the relationships between the angles and sides of right triangles. The Pythagorean theorem and trigonometric functions allow us to calculate unknown sides or angles when certain measurements are known.

2. How Does the Calculator Work?

The calculator uses these fundamental formulas:

Where:

• \( a \) — Length of one leg
• \( b \) — Length of the other leg
• \( c \) — Length of the hypotenuse
• \( \theta \) — Angle opposite side a

Explanation: The calculator takes two legs of a right triangle and calculates the hypotenuse using the Pythagorean theorem and the angle using the arctangent function.

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 lengths of two legs (a and b) in any consistent units. Select whether you want the angle result in degrees or radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if I know the hypotenuse and one leg?
A: You can rearrange the Pythagorean theorem to find the missing leg: \( a = \sqrt{c^2 - b^2} \).

Q2: How accurate are the results?
A: Results are accurate to 4 decimal places for lengths and 2 decimal places for angles in degrees.

Q3: 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.

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: How is the angle calculated?
A: The angle θ is calculated as the arctangent of the ratio of the opposite side (a) to the adjacent side (b).