1. What is Theta?

Theta (θ) is commonly used to represent an angle in a right triangle. In trigonometry, it's often the angle between the hypotenuse and the adjacent side of a right triangle.

2. How to Calculate Theta

When you know the lengths of the opposite side and hypotenuse, you can calculate theta using the arcsine function:

Where:

• \( \theta \) — The angle in radians (converted to degrees for display)
• opposite — Length of the side opposite to the angle
• hypotenuse — Length of the hypotenuse

Explanation: The arcsine function is the inverse of the sine function, returning the angle whose sine is the given ratio.

3. Understanding the Arcsin Function

Details: The arcsine function (asin) returns values between -π/2 and π/2 radians (-90° to 90°). For right triangles, we only consider positive values between 0° and 90°.

4. Using the Calculator

Tips: Enter the lengths of the opposite side and hypotenuse. Both values must be positive numbers, and the opposite side cannot be longer than the hypotenuse.

5. Frequently Asked Questions (FAQ)

Q1: What if my opposite side is longer than the hypotenuse?
A: This is impossible in a right triangle. The hypotenuse is always the longest side. The calculator will not return a result in this case.

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

Q3: Why does the result come in degrees?
A: Degrees are more commonly used in practical applications. The calculation is done in radians internally and then converted.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise, though displayed results are rounded to 2 decimal places for readability.

Q5: What if I know the adjacent side instead of the opposite?
A: You would then use the arccosine function instead: θ = arccos(adjacent/hypotenuse).