1. What is Tan Theta?

Tan theta (tan θ) is a trigonometric function that represents the ratio of the length of the opposite side to the length of the adjacent side in a right-angled triangle. It's one of the primary trigonometric functions along with sine and cosine.

2. How Does the Calculator Work?

The calculator uses the tan theta formula:

Where:

• \( \text{opposite} \) — Length of the side opposite to angle θ (in meters)
• \( \text{adjacent} \) — Length of the side adjacent to angle θ (in meters)

Explanation: The tangent of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side.

3. Importance of Tan Theta Calculation

Details: Tan theta is fundamental in trigonometry and has applications in physics, engineering, navigation, and many other fields. It's used to determine angles, calculate heights, and solve various geometric problems.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides in meters. Both values must be positive numbers. The result is dimensionless since it's a ratio of two lengths.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of tan theta values?
A: Tan theta can range from negative infinity to positive infinity, depending on the angle θ.

Q2: What happens when the adjacent side is zero?
A: Tan theta is undefined when the adjacent side is zero (at 90° and 270°).

Q3: How is tan theta related to other trig functions?
A: Tan theta equals sine theta divided by cosine theta (tan θ = sin θ / cos θ).

Q4: What are practical applications of tan theta?
A: Used in calculating slopes, angles of elevation/depression, and in fields like architecture and physics.

Q5: Can tan theta be greater than 1?
A: Yes, tan theta is greater than 1 for angles between 45° and 90° (and between 225° and 270°).