1. What is a Right Triangle Ratio Calculator?

Definition: This calculator determines the angle (θ) in a right triangle using the tangent ratio of the opposite side to the adjacent side.

Purpose: It helps students, engineers, and designers solve right triangle problems in trigonometry, construction, and navigation.

2. How Does the Calculator Work?

The calculator uses the tangent trigonometric function:

Where:

• \( \theta \) — Angle in degrees
• \( opp \) — Length of side opposite to angle θ
• \( adj \) — Length of side adjacent to angle θ

Explanation: The calculator takes the ratio of opposite to adjacent sides, calculates the inverse tangent (arctangent) to find the angle in radians, then converts it to degrees.

3. Importance of Right Triangle Calculations

Details: These calculations are fundamental in trigonometry, used in fields like architecture, engineering, physics, and computer graphics for angle and distance measurements.

4. Using the Calculator

Tips: Enter the lengths of the opposite and adjacent sides (both must be positive values). The calculator will return the angle θ in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for the sides?
A: The calculator works with any consistent units (meters, feet, etc.). Just ensure both sides use the same unit.

Q2: What's the range of possible angles?
A: The calculator returns angles between 0° and 90° (exclusive) for valid right triangle inputs.

Q3: Can I calculate side lengths if I know the angle?
A: This version calculates angles from sides. For side calculations, you'd need a different version of the calculator.

Q4: How accurate are the results?
A: Results are accurate to two decimal places, sufficient for most practical applications.

Q5: What if I enter zero or negative values?
A: The calculator requires positive values for both sides as lengths cannot be zero or negative.