1. What is Tangent?

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. It's one of the primary trigonometric functions.

2. How Does the Calculator Work?

The calculator uses the tangent formula:

Where:

• \( \theta \) — Angle in the right triangle
• opposite — Side opposite to the angle θ
• adjacent — Side adjacent to the angle θ

Explanation: The tangent function relates the two sides of a right triangle that form the right angle with the non-right angle θ.

3. Importance of Tangent Calculation

Details: Tangent is fundamental in trigonometry, used in various fields including physics, engineering, navigation, and architecture for solving problems involving right triangles.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides in any consistent units. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of tangent values?
A: Tangent can be any real number, from negative to positive infinity, depending on the angle.

Q2: How is tangent different from sine and cosine?
A: While sine is opposite/hypotenuse and cosine is adjacent/hypotenuse, tangent is opposite/adjacent.

Q3: What happens when the adjacent side is zero?
A: Tangent is undefined at 90° and 270° where the adjacent side would be zero.

Q4: Can I use this for non-right triangles?
A: No, this formula is specifically for right triangles. For other triangles, you'd need the Law of Tangents.

Q5: How is tangent used in real-world applications?
A: It's used in calculating heights of buildings, angles of elevation/depression, slope gradients, and more.