Height of a tree from shadows

Aim

To find the height of a tree using similar triangles.

Apparatus

• A 1 m stick
• A measuring tape
• A sunny day

Method

1. Stand the stick upright on level ground.
2. Measure the shadow of the stick, s.
3. At the same moment measure the shadow of the tree, t.
4. Work out height ≈ t ÷ s × 1 m.
5. Repeat at different times of day and take the mean.

Conclusion

The stick and the tree with their shadows form similar triangles, so height ÷ shadow is the same for both. The tree is t ÷ s metres tall, whatever the time of day.