1. What is the Theta Angle?

The theta angle (θ) is the angle between the adjacent side and hypotenuse in a right-angled triangle. It's calculated using the inverse cosine (arccosine) of the ratio between the adjacent side and the hypotenuse.

2. How Does the Calculator Work?

The calculator uses the theta angle formula:

Where:

• \( adj \) — Length of the adjacent side (units)
• \( hyp \) — Length of the hypotenuse (units)
• \( \theta \) — Angle in radians

Explanation: The arccosine function returns the angle whose cosine is the given ratio of adjacent side to hypotenuse.

3. Importance of Theta Angle Calculation

Details: Calculating angles in right triangles is fundamental in trigonometry, physics, engineering, and computer graphics. It helps in determining unknown angles when side lengths are known.

4. Using the Calculator

Tips: Enter positive values for both adjacent side and hypotenuse. The adjacent side must be less than or equal to the hypotenuse (as cosine values range between -1 and 1).

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for non-right triangles?
A: No, this formula specifically applies to right-angled triangles. For other triangles, use the Law of Cosines.

Q2: How do I convert radians to degrees?
A: Multiply the radian value by (180/π) to convert to degrees.

Q3: What if my adjacent side is longer than hypotenuse?
A: This is impossible in a right triangle. The hypotenuse is always the longest side.

Q4: What's the range of theta angle values?
A: In a right triangle, theta ranges from 0 to π/2 radians (0° to 90°).

Q5: Can I use negative values?
A: No, side lengths must be positive values.