Question

You are driving into St. Louis, Missouri and in the distance you see the famous Gateway–to–the–West arch. This monument rises to a height of 192 m. You estimate your line of sight with the top of the arch to be 2.0° above the horizontal. Approximately how far (in kilometers) are you from the base of the arch?

Answer 1

The situation is diagrammed in Figure 1.12. (Of course the ground is not exactly flat and your eyeballs are not quite at ground level but these details don’t make much difference.) If the distance of the car from the base of the arch is x then we have

The car is about 5.50 km from the base of the arch.