The Question
Alice wants to take a picture of a historical building that is wide but not tall. From available references, she is able to find out that the building is 33 metres wide. She plans to take the picture standing directly in front of it, at a point perpendicular to the midpoint of the building. She is using a moderately wide-angle lens which provides an angle of coverage of 64◦.
Alice sketches the situation as in Figure 7, where all lengths are measured in metres. The point A represents Alice’s position. Points B and C are at each end of the building. Point D is the midpoint of the building. The length of AB is equal to the length of AC. The angle BAD is 32◦.
How far from the midpoint D should Alice stand in order to be able to take a picture of the whole building? (You can assume that the height of the building is not an issue)