Solving for UT Length and Area of Nonrectangular Land Plot | Geometry/Trig Help

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To solve for the length of side UT and the area of a nonrectangular plot of land, the law of sines and law of cosines are essential tools. The law of cosines can be used to relate the sides and angles of the triangle formed by points R, S, and T, while the law of sines can help find the remaining sides and angles. Drawing a diagram can aid in visualizing the relationships between the sides and angles. With the given measurements, applying these laws will lead to the necessary calculations. This approach will effectively address the surveying challenge presented.
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A surveyer is required to survey a nonrectangular plot of land but is unable to measure side UT directly. The following data are taken:
RU= 130.0 m
RS= 120.0 m
ST=90.0m
Angle RST= 115 degrees
Angle RUT = 100 degrees

Calculate the length of side UT and area of the plot.

Again I haven't taken any geometry or trig in years and just need help starting the problems(I have a few to post)
 

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hello UR5,
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 definately 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.
 
Thanks that worked out well.
 

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