How Do You Solve the Ambiguous Triangle Case in Trigonometry?

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Homework Help Overview

The problem involves determining the possible distances between two towns, Teatown and Coffee Town, given their distances from a third town, Kettletown, and an included angle. The context is trigonometry, specifically dealing with ambiguous cases in triangle formation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the possibility of drawing two triangles based on the given data and question the application of the sine formula. There are inquiries about the uniqueness of angle values and the implications of the included angle on triangle construction.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the drawing of triangles and the application of trigonometric formulas, but no consensus has been reached on the approach to take.

Contextual Notes

There are indications of uncertainty regarding the correct setup of the triangle and the application of trigonometric principles, as well as some informal exchanges about spelling and terminology.

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Homework Statement


kettletown is 27km from teatown and 32km from coffee town. The angle from kettletown to coffee town to teatown is 29o. Determine the two possible distances between teatown and coffee town.

Homework Equations

The Attempt at a Solution


The only problem I'm having is trying to draw the triangle I am insure of how to do it.
 
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You try; two triangles can be drawn with this data. Use sine formula? Do you get only one value of theta for angle opposite to 32 side, angle opposite to 27 is 29?. Think it over while drawing! When included angle is given only one triangle can be drawn as cosine formula fixes the third side.
 
Veronica_Oles said:

Homework Statement


kettletown is 27km from teatown and 32km from coffee town. The angle from kettletown to coffee town to teatown is 29o. Determine the two possible distances between teatown and coffee town.

Homework Equations

The Attempt at a Solution


The only problem I'm having is trying to draw the triangle I am insure of how to do it.
Just draw an arbitrary triangle, and denote the vertices by K, T, C, representing the towns.
 
Veronica, R u not well versed with sine and cosine formulas for triangles?
 
Let'sthink said:
Veronica, R u not well versed with sine and cosine formulas for triangles?
You misspelled the words "Are" and You".
 
sorry for the misspellings of are and you!
 

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