📐 Angle Between Two Lines Calculator
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📌 Understanding Angle Between Two Lines
The angle between two lines in a 2D plane is calculated using the formula:
θ = arctan(|(m₂ – m₁) / (1 + m₁m₂)|)
📌 Examples of Angle Calculation
| Slope of Line 1 (m₁) | Slope of Line 2 (m₂) | Angle (θ in degrees) |
|---|---|---|
| 1 | -1 | 90° |
| 2 | 0.5 | 26.57° |
| 3 | 1 | 45° |
🔧 Practical Applications of Angle Calculation
1. Engineering & Architecture: Used to analyze structural alignments and design angles.
2. Physics & Mechanics: Helps in calculating motion trajectories and angles of reflection.
3. Robotics & AI: Essential for path planning and geometric computations in navigation.
❓ FAQs
Q1: How do I find the angle between two lines?
✅ Use the formula **θ = arctan(|(m₂ – m₁) / (1 + m₁m₂)|)**, where m₁ and m₂ are the slopes.
Q2: What if one of the lines is vertical?
✅ If a line is vertical, its slope is **undefined**, and the angle between a vertical and a non-vertical line is **90°**.
Q3: Can I find the angle using coordinates?
✅ Yes, first find the slopes using **m = (y₂ – y₁) / (x₂ – x₁)** and then use the formula.
Q4: Where is angle calculation used?
✅ It is widely used in **architecture, engineering, robotics, and physics**.
Q5: What does a 90° angle indicate?
✅ A 90° angle means the two lines are **perpendicular** to each other.