Solve a Triangle using Trigonometry

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Homework Help Overview

The discussion revolves around solving a triangle using trigonometric principles, specifically focusing on finding angle DCB (denoted as x) given certain conditions related to the triangle's sides and angle bisector.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the Law of Sines and share their attempts at formulating equations based on the triangle's properties. There are questions about the correctness of calculations and the interpretation of angle measures.

Discussion Status

Some participants have provided guidance on checking calculations and suggested writing out steps for clarity. There is an acknowledgment of differing angle measures and the implications of those choices on the solution.

Contextual Notes

There is mention of a specific solution provided in a textbook, which has led to discussions about potential mistakes in calculations and the validity of angle measures used in the problem.

okh
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You are right by guessing Law of sines. Why don't you show what work you've done till now and where exactly you're stuck?
 
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okh said:
I've written this system of equations:
http://img13.imageshack.us/img13/9355/imagenxvc.jpg

But I get
3cos^2x+sin^2x-2cosx=0 and the solution of the poblem that the book gives me is ∏/5.

The first three equations you've written down are correct. The answer is indeed pi/5. Check your calculation again. If you still don't find your mistake, write down your step by step solution, and i'll tell you where you're going wrong.
 
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praharmitra said:
The first three equations you've written down are correct. The answer is indeed pi/5. Check your calculation again. If you still don't find your mistake, write down your step by step solution, and i'll tell you where you're going wrong.
I've found my mistake, now I get 3cos^2x-sin^2x-2cosx=0 and the solution is pi/5.
Thank you very much for helping!
 
A word of advice, though. It's never a good idea to mix two different angle measures. Since you started in degrees, you should finish in the same. So the answer is x = 36 degrees.
 
I agree, with Curious3141. You might also want to justify why you rejected the other value of x, which is 108 degrees.

I see 2 reasons:
1. Since x is an acute angle from the figure, x cannot be 108 degrees.
2. If you evaluate the angle CAD, using x=108 degrees, you'll get a negative value, which is not possible.

I hope that helped you a little bit.
 

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