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

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In summary, the conversation discusses a surveyer needing to measure a nonrectangular plot of land and provides data such as the lengths of RU and RS, the angle RST, and the angle RUT. The problem can be solved using either the law of sines or law of cosines equations to form oblique triangles and find the length of side UT. It is suggested to draw a shape resembling a rectangle to visualize the opposite sides.
  • #1
ur5pointos2sl
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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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  • #2
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.
 
  • #3
Thanks that worked out well.
 

1. What is the difference between Euclidean Geometry and Non-Euclidean Geometry?

Euclidean Geometry is the study of flat, two-dimensional shapes and their properties, while Non-Euclidean Geometry is the study of curved and higher-dimensional shapes. In Euclidean Geometry, the Parallel Postulate holds true, stating that two lines will never intersect. However, in Non-Euclidean Geometry, this postulate does not hold true, allowing for the possibility of intersecting lines.

2. How does the Pythagorean Theorem relate to Trigonometry?

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In Trigonometry, this theorem is used to find the length of a missing side or angle in a right triangle using trigonometric functions such as sine, cosine, and tangent.

3. What is the Law of Sines and how is it used in Trigonometry?

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is equal for all three sides. This law is used in Trigonometry to solve for missing sides and angles in any triangle, not just right triangles.

4. How are radians and degrees related in Trigonometry?

Radians and degrees are both units of measurement for angles. In Trigonometry, radians are often preferred over degrees because they provide a more natural measure for angles in circular functions. One radian is equal to 180/π degrees.

5. Can Trigonometry be used in real-life applications?

Yes, Trigonometry has many real-life applications, such as in engineering, physics, and astronomy. It is used to calculate distances, angles, and forces in various structures and systems. It is also used in navigation and mapping, as well as in the study of waves and oscillations.

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