Heights & Distances

Measuring what you can’t reach

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Height = horizontal distance × tan(angle of elevation).
• Angles of depression from above equal angles of elevation from below.
• Two sightings $d$ apart give $h = \frac{d}{\cot\alpha - \cot\beta}$.

Steps

1. Angles of elevation
2. Back away
3. From the cliff
4. Shadow of a flagpole
5. When you can’t reach the base
6. Measuring Everest
7. Two sightings