Interesting maximization problem

[FermatPell]

Homework Statement

Imagine that you are lost in the desert. You are equipped with a compass. You can use your compass to measure angles, but not the distances. There is a road (going from east to west) and you're going northwards. Suddenly, you spot a truck (on a road, going to west) at angle theta with respect to north. In which direction should you run to maximize chances of stopping the truck (the truck stops instantly if you block the road so it can't go any further).

Homework Equations

The Attempt at a Solution

 

[NateD]

You should run in the direction of the truck, at an angle theta with respect to north. Since the truck is going west, it will be travelling in a direction perpendicular to the road and thus the angle between you and the truck would be 90 degrees. Therefore, you should run in the direction of the truck at an angle theta with respect to north in order to maximize your chances of stopping the truck.