1. What is Angle Theta?

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

2. How Does the Calculator Work?

The calculator uses the arccosine formula:

Where:

• \( \theta \) — Angle in degrees
• adjacent — Length of the side adjacent to the angle (meters)
• hypotenuse — Length of the hypotenuse (meters)

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

3. Importance of Angle Calculation

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

4. Using the Calculator

Tips: Enter the adjacent side length and hypotenuse in meters. Both values must be positive numbers, and the adjacent side cannot be longer than the hypotenuse.

5. Frequently Asked Questions (FAQ)

Q1: What if my adjacent side is longer than the hypotenuse?
A: In a right triangle, the hypotenuse is always the longest side. If you get this result, check your measurements.

Q2: What units should I use?
A: The calculator uses meters, but any consistent unit will work as the ratio is unitless.

Q3: Can I calculate the angle if I know the opposite side?
A: Yes, but you would use the arcsine function instead: θ = arcsin(opposite/hypotenuse).

Q4: How precise is this calculation?
A: The calculation is mathematically precise, limited only by the precision of your input measurements.

Q5: Can I use this for non-right triangles?
A: No, this specific formula only works for right-angled triangles. For other triangles, use the Law of Cosines.