1. What is the Tangent Ratio?

The tangent ratio is a fundamental trigonometric function that relates the lengths of the opposite and adjacent sides of a right triangle to one of its non-right angles. It's defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

2. How Does the Calculator Work?

The calculator uses the tangent formula:

Where:

• \( \theta \) — Angle in the right triangle (in degrees)
• opposite — Length of the side opposite to angle θ
• adjacent — Length of the side adjacent to angle θ

Explanation: The calculator first computes the tangent ratio, then uses the arctangent function to determine the angle in degrees.

3. Importance of Tangent Ratio

Details: The tangent ratio is essential in trigonometry, physics, engineering, and navigation. It helps solve problems involving right triangles, slopes, angles of elevation/depression, and more.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides of your right triangle. Both values must be positive numbers. The calculator will provide the tangent ratio and the corresponding angle in degrees.

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, as the angle approaches 90° or -90°.

Q2: What if my triangle isn't right-angled?
A: The tangent ratio only applies to right triangles. For other triangles, you would need to use the Law of Tangents or other trigonometric laws.

Q3: How accurate is the angle calculation?
A: The angle is calculated to within 0.1 degrees, which is sufficient for most practical applications.

Q4: Can I use this for slope calculations?
A: Yes, the tangent of an angle equals the slope of a line making that angle with the x-axis.

Q5: What units should I use for the side lengths?
A: The units don't matter as long as both sides use the same units (the ratio is dimensionless).