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Get Full Access to Precalculus With Trigonometry: Concepts And Applications - 1 Edition - Chapter 6-7 - Problem 19
Get Full Access to Precalculus With Trigonometry: Concepts And Applications - 1 Edition - Chapter 6-7 - Problem 19

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# Surveying 4: Surveyors find the area of an irregularly shaped tract of land by taking ISBN: 9781559533911 468

## Solution for problem 19 Chapter 6-7

Precalculus with Trigonometry: Concepts and Applications | 1st Edition

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Problem 19

Surveying 4: Surveyors find the area of an irregularly shaped tract of land by taking field notes. These notes consist of the length of each side and information for finding each angle measure. For this problem, starting at one vertex, the tract is divided into triangles. For the first triangle, two sides and the included angle are known (Figure 6-7m), so you can calculate its area. To calculate the area of the next triangle, you must recognize that one of its sides is also the third side of the first triangle and that one of its angles is an angle of the polygon (147 in Figure 6-7m) minus an angle of the first triangle. By calculating this side and angle and using the next side of the polygon (15 m in Figure 6-7m), you can calculate the area of the second triangle. The areas of the remaining triangles are calculated in the same manner. The area of the tract is the sum of the areas of the triangles. Figure 6-7m a. Write a program for calculating the area of a tract using the technique described. The input should be the sides and angles of the polygon. The output should be the area of the tract. b. Use your program to calculate the area of the tract in Figure 6-7m. If you get approximately 1029.69 m2, you can assume that your program is working correctly. c. Show that the last side of the polygon is 30.6817 m long, which is close to the measured value of 31 m. d. The polygon in Figure 6-7m is a convex polygon because none of the angles measures more than 180. Explain why your program might give wrong answers if the polygon were not convex.

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##### ISBN: 9781559533911

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