Constructing accurate diagrams of word problem- Trig

In summary: Once I get a drawing going, I can go from there. Making the actual drawing seems to be where the ambiguity is.
  • #1

opus

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Homework Statement


A canoe is floating down a creek. The canoe is first spotted 80 feet away. 7 minutes later the canoe is 45 feet away, making a 40° angle between the two sightings.
How far did the canoe travel?

Homework Equations


Law of Sines and Law of Cosines

The Attempt at a Solution



This question is more in terms of constructing a proper diagram. I have two different drawings, and I'm really just looking for guidance as to which drawing is accurate to the given problem, and why the other isn't. They both seem to represent the problem, but they both don't seem to be saying the same thing.
Please see my attached image. Thank you!
 
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  • #2
Attached image
 

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  • #3
opus said:

Homework Statement


A canoe is floating down a creek. The canoe is first spotted 80 feet away. 7 minutes later the canoe is 45 feet away, making a 40° angle between the two sightings.
How far did the canoe travel?

Homework Equations


Law of Sines and Law of Cosines

The Attempt at a Solution



This question is more in terms of constructing a proper diagram. I have two different drawings, and I'm really just looking for guidance as to which drawing is accurate to the given problem, and why the other isn't. They both seem to represent the problem, but they both don't seem to be saying the same thing.
Please see my attached image. Thank you!
I think your first drawing is more appropriate. The second drawing seems to imply that the observer is on a high bank looking down at the canoe.
 
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  • #4
Mention any details about angle of elevation or depression? None? All done in the same plane. Your upper diagram fits.
 
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  • #5
Ok thanks guys. Once I get a drawing going, I can go from there. Making the actual drawing seems to be where the ambiguity is.
 
  • #6
opus said:
Ok thanks guys. Once I get a drawing going, I can go from there. Making the actual drawing seems to be where the ambiguity is.
The description is not really ambiguous. The straightforward interpretation leads to the single triangle shown in the first picture. No mention of angles of elevation nor depression were given. Check again post #3.
 
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  • #7
I guess I just need to do more of them. So the second drawing would relate to angle of depression I see.
 
  • #8
opus said:
I guess I just need to do more of them. So the second drawing would relate to angle of depression I see.
BINGO! Right on target! Do MORE exercises; not fewer. Keep up practicing the many exercises, and from different books, for the same topics as you study and with experience you may become familiar with some types of exercises and they become easier to analyze and solve.
 
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  • #9
Thanks guys.
 

What is the purpose of constructing accurate diagrams of word problem- Trig?

The purpose of constructing accurate diagrams of word problems in trigonometry is to visually represent the given information in a clear and organized manner. This allows us to better understand the problem and develop a solution strategy.

How do I construct an accurate diagram for a word problem in Trig?

To construct an accurate diagram, start by identifying the given information and labeling it on the diagram. Then, use the appropriate trigonometric ratios to find missing information and label it on the diagram. Make sure to use the correct scale and include all relevant angles and sides.

What should I do if I am unsure of how to label the diagram in a word problem- Trig?

If you are unsure of how to label the diagram, go back to the given information and make sure you understand what it is asking for. You can also use the Pythagorean Theorem to find missing sides or angles that are not directly given in the problem.

Why is it important to accurately label the diagram in a word problem- Trig?

Accurately labeling the diagram is important because it ensures that we are using the correct information and trigonometric ratios to solve the problem. It also helps us to avoid making mistakes and arriving at an incorrect solution.

Are there any common mistakes to avoid when constructing diagrams for word problems in Trig?

Yes, some common mistakes to avoid include using the wrong scale, forgetting to label all relevant information, and not using the correct trigonometric ratios. It is important to double check your diagram and solution to ensure accuracy.

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