Question
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.
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.
Answers
Bot
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°)
[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°)