Question

A surveyor standing at A notices two posts B and C on the opposite side of a canal. The posts are 120m apart. If the angle of sight between the posts is 37, how wide is the canal?

Answer 1

Unfortunately there isn't enough information.

Check out the diagram below. We have segment BC equal to 120 meters long. Points B, C, D and E are all on the edge of the same circle. According to the inscribed angle theorem, angles BDC and BEC are congruent. This shows that the surveyor could be at points D or E, or the surveyor could be anywhere on the circle. There are infinitely many locations for the surveyor to be at, which leads to infinitely many possible widths of this canal.