Example: Consider the following scenario:

While on a road trip, you find yourself traveling along a stretch of highway that is running directly south for many miles. Off in the distance, you see an interesting looking mountain. You might ask yourself: "how far away is that mountain?" 

To determine this--assuming you have the requisite tools--you stop for a moment and measure that the mountain's peak measures \(40^\circ\) south of east. After driving for two hours and 120 miles due south, you stop and repeat the measurement. This time, the mountain peak is \(15^\circ\) south of east.

Based on those observations, how far are you from the mountain when you take the second measurement?

Advanced: suppose that the road isn't running due south, but instead runs at a heading of \(5^\circ\) west of south. Presuming the same measurements above (including the distance traveled along the road) how far away from the mountain are you when you take the second measurement?