The diagram below shows the two possible configurations of Sam's triangular piece of land. The first configuration (on the left) has a first side of length x, and the second configuration (on the right) has a first side of length y.
[Diagram]
The area of the first configuration is given by A1 = (1/2)x(340)sin(24°).
The area of the second configuration is given by A2 = (1/2)y(340)sin(24°).
Since the length of the first side is unknown, the two possible areas cannot be calculated to the nearest square foot. However, the two possible areas can be expressed as a function of x and y, respectively:
A1 = (1/2)x(340)sin(24°)
A2 = (1/2)y(340)sin(24°)
Sam owns a triangular piece of land on which the tax collector wishes to determine the correct property tax. Sam tells the collector that “the first side lies on a straight section
of road and the second side is a stone wall. The wall meets the road at a 24-degree angle.
The third side of the property is formed by a 180-foot-long fence, which meets the wall at a point that is 340 feet from the corner where the wall meets the road.” After a little
thought, the tax collector realizes that Sam’s description of his property is ambiguous,because there are still two possible lengths for the first side. By means of a clear diagram,
explain this situation, and calculate the two possible areas, to the nearest square foot.
1 answer
1 answer