Tangent & Slopes

The angle between two lines

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Slope $= \tan(\text{angle of inclination})$.
• $\tan(A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A\tan B}$.
• Angle between lines: $\tan\theta = \left|\frac{m_2 - m_1}{1 + m_1 m_2}\right|$; perpendicular when $m_1m_2 = -1$.

Steps

1. Slope is a tangent
2. tan 75°
3. Angle between lines
4. Make 45°
5. Perpendicular
6. A surprising sum