1. What is the Tangent Ratio?

The tangent ratio is a fundamental trigonometric function that relates the opposite side to the adjacent side of a right-angled triangle. It's defined as the ratio of the length of the opposite side to the length of the adjacent side for a given angle in a right triangle.

2. How Does the Calculator Work?

The calculator uses the tangent ratio formula:

Where:

• \( \tan \theta \) — Tangent of angle θ (dimensionless)
• opposite — Length of side opposite to angle θ (meters)
• adjacent — Length of side adjacent to angle θ (meters)

Explanation: The tangent ratio is particularly useful in right triangle trigonometry for finding unknown side lengths or angles.

3. Importance of Tangent Ratio

Details: The tangent function is essential in various fields including physics, engineering, navigation, and architecture. It helps in calculating heights of objects, angles of elevation and depression, and in solving problems involving right triangles.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides in meters. Both values must be positive numbers. The calculator will compute the tangent ratio, which is dimensionless.

5. Frequently Asked Questions (FAQ)

Q1: What's the range of tangent values?
A: The tangent function can produce any real number value, 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. Tangent can also be expressed as sine divided by cosine.

Q3: What happens when the adjacent side is zero?
A: The tangent ratio becomes undefined (infinite) when the adjacent side is zero, which occurs at 90° in a right triangle.

Q4: Can I use this for non-right triangles?
A: The tangent ratio specifically applies to right triangles. For other triangles, you would need to use the Law of Tangents or divide them into right triangles.

Q5: How can I find the angle from the tangent ratio?
A: You can use the arctangent (inverse tangent) function to find the angle when you know the tangent ratio.