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.

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.2: Law Of Cosines
Problem 3ECP: In a softball game, a batter hits a ball to dead center field, a distance of 240 feet from home...
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.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.

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