Bearings Project

Question

I have NO idea how to do any of this. I've been trying for 2 weeks without any luck.

 

Bearings: (Start on the right of the paper) Beginning at the first survey marker (A), proceed 227.0 feet bearing due South to marker B. At marker B, turn down West and proceed 127.0 feet to marker C. At marker C, turn to a bearing N13.2°W and proceed 151.2 feet to marker D. At marker D, turn on a bearing of N42°E and proceed 122.6 feet to marker E. At marker E, turn to bearing S81.9°E and proceed 80.3 feet, which returns to the point of beginning.

 

Now, for the actual task.

 

Task: Make a sketch of the property (it need not be a scale drawing). Calculate the exact area of the tract. You have discovered that in order to develop the property, the company will have to run a gas line from marker D to marker A, and a water line from Marker C to Marker A. Report the exact lengths of the gas and water lines. Excavating for the lines will cost $23/foot (same cost for gas or water). Installing the water will cost $.35 per foot, and installing the gas line will cost $1.20 per foot. Estimate the total cost for installing the gas and water lines. 

 

Hints: Begin drawing near the upper right corner of your paper. To find the area, split the irregular pentagon up into three triangles. Use the laws of sines and cosines to find the lengths of the sides you construct. Find the area of the triangle using the formula

A = 1/2 bc sin C

Answer 1

I just joined Wyzant this past weekend, so sorry for late response. 

 

If if you need a drawing, I can provide one. Let me know. 

 

Water line is 260.1 ft, by Pythahorean Theorem. 

 

Gas line is 180.2 ft, by law of cosines. 

 

Area of lower triangle is 14414.5, by 1/2(base)(height).

 

Area of middle triangle is 13286.1, by Heron's formula. 

 

Area of top triangle is 4085.6, by 1/2(DE)(AE)sinE.

 

TOTAL AREA = 31786.2 ft².

 

Total cost= $10,434.18. 

 

If this is correct, I hope this demonstrates my ability, and you'll call on me in the future. 

Answer 2

The solution to this complex problem requires a knowledge of how bearings relate to angles. Bearings begin at due North, and proceed clockwise to form a circle, which equals 360^o.

 

The solution requires more room than can be entered on this page.

 

Please write to me, and I will be able to send the solution to you.