Trigonometry: Another Statics Problem

In summary, the conversation discusses a surveying error of 0.10 degrees when setting an iron pin in the corner of a 200 ft by 80 ft subdivision lot. The attempt at a solution involves treating the left part of the lot as a right triangle and using the tangent function to find the distance by which the correct pin is off from the true corner, resulting in an error of approximately 0.349 feet.
  • #1
blixel
52
1

Homework Statement


A subdivision lot is 200 ft long by 80 ft wide. A surveying crew made an error of 0.10 degrees when setting the iron pin in the corner of the lot shown. By what distance is the correct pin off of the true corner?

Problem%2014_zpsjucnp3ue.png


Homework Equations


I think I'm doing this one right also, but it's an even numbered problem so I can't check my answer.

The Attempt at a Solution


I'm treating the left part of the image as a right triangle. I'm saying that theta=0.10 degrees, and theta is located at the top of the triangle. So the opposite is the short piece at the bottom, and that's what I'm trying to find.

tan(theta)=opposite/adjacent

Adjacent is along the side, and it's 200 feet.

opposite=200*tan(0.10)~=0.349 feet.

So, if I've done this right, the distance is off by 0.349 feet.
 

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  • #2
That's what I get, as well.
 
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1. What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships and properties of triangles and the trigonometric functions (sine, cosine, and tangent).

2. How is trigonometry used in statics problems?

Trigonometry is used in statics problems to calculate the relationships between forces and angles in a system. It is especially useful in solving problems involving right triangles.

3. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. These functions represent the ratios of the sides of a right triangle, and they can be used to calculate the lengths of unknown sides or the measure of angles.

4. How do you apply trigonometry to solve a statics problem?

To apply trigonometry to solve a statics problem, you first need to identify the right triangle(s) within the system. Then, you can use the trigonometric functions to calculate the unknown sides or angles by setting up and solving equations.

5. What are some real-world applications of trigonometry in statics?

Trigonometry is used in many real-world applications of statics, such as engineering and architecture. It can be used to design structures, calculate the forces acting on them, and ensure their stability.

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