Solving a Trig Word Problem Involving Pipes

In summary, the problem is to find the length of a metal band that is tightly tied around six identical pipes with a radius of 1 foot each. A strategy for solving this problem is suggested, involving dividing the figure in half and finding the measures of two equal arcs and a yellow line. The suggestion is to divide the yellow line into three parts and use knowledge of cosines and sines on a circle. However, it is pointed out that this problem can be solved without trigonometry by considering the outline of the figure and replacing the straight segments with a single point. The lengths of the curved segments and the straight lines can then be easily determined.
  • #1
Miike012
1,009
0

Homework Statement



Six Identical pipes, each with radius of 1 foot are ties tightly together with a metal band... Find the length of the metal band...

I posted a picture...

My strategy is dividing the figure in half
Then finding the measure of the two arcs in red ( which should be equal)
Then finding the measure of the yellow line..
Once I find that... I can multiply it by three...
I am just not sure of how to do it...
 

Attachments

  • MAATH.jpg
    MAATH.jpg
    13 KB · Views: 455
Physics news on Phys.org
  • #2
Well, it looks to me as if x=30 degrees, but that's just an educated guess. And I recommend dividing the yellow line into three parts, the part above the bottom left circle, the part above the middle left circle, and the part above the upper circle. The middle part has an easy to calculate length, and the two outer parts will require some knowledge of cosines and sines on a circle.
 
  • #3
This requires no trig. Just consider the outline. If you replace the straight segments with a single point, what are you left with?

So the length of the curved segments are taken care of. It's easy to see the straight lines are all the same length. So, just look at the bottom one. How does it compare to the radius of the pipes?
 

FAQ: Solving a Trig Word Problem Involving Pipes

What are the key elements to consider when solving a trig word problem involving pipes?

The key elements to consider when solving a trig word problem involving pipes are the length of the pipe, the angle at which the pipe is positioned, and the height of the pipe above the ground. These elements will help you determine the necessary trigonometric functions to use in your calculations.

How do I determine the appropriate trigonometric function to use in a pipe word problem?

To determine the appropriate trigonometric function, you need to look at the given information in the problem and identify the sides and angles involved. If you are given the length of the pipe and the angle at which it is positioned, you will likely need to use the sine or cosine function. If you are given the height of the pipe and the angle of elevation, you will need to use the tangent function.

Can I use the Pythagorean theorem in a trig word problem involving pipes?

Yes, the Pythagorean theorem can be used in a trig word problem involving pipes. If you are given two sides of a right triangle, you can use the Pythagorean theorem to find the length of the third side, which may be needed in your calculations.

What are some common mistakes to avoid when solving a trig word problem involving pipes?

Some common mistakes to avoid when solving a trig word problem involving pipes include using the wrong trigonometric function, forgetting to convert between degrees and radians, and incorrectly setting up the trigonometric ratio. It is important to carefully read the problem and identify all necessary information before beginning your calculations.

How can I check my answer when solving a trig word problem involving pipes?

You can check your answer by drawing a diagram of the problem and comparing your calculated values to the given information. You can also use a calculator to verify your trigonometric calculations. If possible, it is always helpful to double-check your work to ensure accuracy.

Similar threads

Trig Identities -- example problem confusion
Replies
10
Views
2K
Trig Word Problem: Finding Height of a Baloon
Replies
4
Views
7K
Puzzling Trig Problem Need Help.
Replies
4
Views
2K
Small trig substitution problem.
Replies
5
Views
2K
Using a Problem Solving Technique for a simple word problem
Replies
24
Views
2K
Solving a Trig Word Problem: Mountain Height
Replies
3
Views
14K
Solving "2(sinA+cosB)sinB=3-cosB" Trig Problem
Replies
3
Views
2K
How Do I Solve Trigonometry Word Problems for My Exam?
Replies
3
Views
4K
Arc length of intersecting circles
Replies
3
Views
2K
What is the Length of a Rope When Two Pipes are Tied Together?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top