### Trigonometry: Triangles to Functions

Bigger picture

Latitude can be measured using the position of the star Polaris above the horizon because that position changes as you move north or south, that is, as you vary your latitude. For longitude this isn’t the case: the position of Polaris does not change as you move east or west, varying your longitude. You can see this in the two-dimensional picture below. The points $P$ and $Q$ lie on different meridians, but the angles arising from the position of Polaris are the same.
What does change as you move east or west is the time of day. For every $15^{\circ}$ of longitude you move eastwards, the local time moves one hour forwards, and for every $15^{\circ}$ you move westwards the local time moves back by an hour. Therefore, if you know your local time and the time at Greenwich, you can use the difference to work out your longitude. Finding your local time is easy even if you haven’t got a clock: you simply observe the position of the Sun. The only way to know the time at Greenwich, however, is to carry a clock with you.