# How do you measure the circumference of the earth using sun angles?

Feb 1, 2016

This is a bit tricky...!

#### Explanation:

You need two spots on the surface of the Earth, A and B.
When standing at A you produce a shadow while standing at B (at the same hour of the day, say, midday) you do not produce a shadow.

You can evaluate, from trigonometry, the angle $\theta$ using your height $h$ and the length of the shadow $l$ as:
$\theta = \arctan \left(\frac{l}{h}\right)$
and knowing the arclength $s$ you can find the radius $r$ using the fact that:
$s = r \cdot \theta$
giving:
$r = \frac{s}{\theta}$
and then use $C = 2 \pi r$ for the circumference.

Hope it is understandable...