An engineer is required to survey a nonrectangular plot of land but is unable to

Question

An engineer is required to survey a nonrectangular plot of land but is unable to measure side UT directly (see Figure 2.11). The following data are taken:                 RU=121.0m, RS=116.0m, ST=83.5m, angle RST= 113 degrees, and angle RUT= 82 degrees.Calculate the length of side UT and the area of the plot.

I set up two triangles in the problem and used law of cosines to find length of RT i got 167.3245153m. I then used this side as the hypotenuse of the triangle RUT and used law of cosines again to find the 3rd side of RUT which is TU (UT) at 134.4527331m. With all this information I assumed find the area would be easy, I just wanted to know if my answers were correct for this first part of the question, and if they are not where did I go wrong.

Explanation / Answer

I believe that for this problem, the equation that will help you is either the law of sines or law of cosines equations. This will help you to form oblique triangles and find out the length of the line going through the shape, which will help in finding out the other two sides.

Law of cosines= C2=a2+b2-2ab(cosC)

Law of sines= sinA/a=sinB/a=sinC/a (captial A= angle A, lower case a=side a)

This should definetly get you headed in the correct direction. If you need to, draw a shape that resembles a rectangle, just so you can get an idea of where the opposite sides would be and all that.

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