Discussion Overview
The discussion revolves around finding the lengths of the sides of a right spherical triangle given its angles, specifically one angle of 90 degrees and the other two angles measuring 50 and 70 degrees. Participants explore various formulas and approaches related to spherical triangles, including the sine formula, cosine formula, polar cosine formula, cotangent formula, and Napiers formula.
Discussion Character
- Exploratory
- Technical explanation
- Homework-related
Main Points Raised
- One participant seeks assistance in solving for the lengths of the sides of a spherical triangle given the angles, expressing uncertainty about where to begin.
- Another participant suggests looking up Girard's theorem as a potential aid in the problem.
- A later reply clarifies that Girard's theorem relates to the area of a spherical triangle, questioning whether finding the area is necessary to determine the side lengths.
- Another participant introduces the Haversine formula as relevant to the problem, indicating a shift in focus from area to arc length.
- One participant expresses confusion about applying the Haversine formula, particularly regarding the variables involved and how to proceed without knowing the lengths of sides a, b, or c.
Areas of Agreement / Disagreement
Participants do not appear to reach a consensus on the best approach to solve the problem, with multiple competing views on which formulas and theorems are applicable.
Contextual Notes
There is uncertainty regarding the relationship between the area of the triangle and the lengths of the sides, as well as the application of the Haversine formula without known side lengths.
Who May Find This Useful
Individuals interested in spherical geometry, particularly those looking to solve problems involving spherical triangles and their properties.