I am researching sundials and the maths behind them. For horizontal sundials (ones that stand perpendicular to the equator) there is a formula to compute the hour angles (the angle between the shadow at noon hour [which is always to the true north] and the shadow at hour $t$): $$\tan(\theta)=\sin(L)\tan(15^\circ\times t)$$ in which
- $\theta$ is the angle between the shadow at noon hour and the shadow at $t$ hour;
- $L$ is the latitude;
- $t$ is the hour you're computing the hour angle for.
I don't understand the intuition behind this formula. Purely mathematically (geometrically) seen, how does it work?
I'm familiar with spherical geometry.