How Do You Solve the Ambiguous Triangle Case in Trigonometry?

  • Thread starter Thread starter Veronica_Oles
  • Start date Start date
  • Tags Tags
    Triangle
AI Thread Summary
To solve the ambiguous triangle case in trigonometry, the problem involves determining the distances between Teatown and Coffee Town given the distances from Kettletown and an included angle. Two triangles can be formed with the provided data, leading to two possible solutions for the distance between the towns. The sine and cosine rules are essential for calculating the unknown sides and angles. Drawing the triangle accurately is crucial for visualizing the problem and applying the correct formulas. Understanding these concepts will help in finding the two potential distances effectively.
Veronica_Oles
Messages
141
Reaction score
3

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.
 
Physics news on Phys.org
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!
 

Similar threads

Prove the sums of the angles of any given triangle = 180°
Replies
12
Views
3K
Solving an oblique triangle. Looking for a correctness check
Replies
3
Views
2K
Area of Outer Triangle composed of two inner triangles
Replies
15
Views
3K
Triangle determined by arithmetic and geometric sequences
Replies
7
Views
2K
Finding the Radius of a Tangent Circumference in a Right Triangle
Replies
9
Views
2K
Maximum area of triangle inside a square
Replies
3
Views
3K
Trigonometry, area of triangle
Replies
10
Views
3K
Isosceles Triangles with Congruent Lateral Sides
Replies
5
Views
3K
What is 2nd Sine? Solving a Triangle with 13.5 Hypotenuse
Replies
17
Views
4K
(Rigorously) Prove that two medians of a triangle intersect
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top