Supplementary Angles for Spherical Trigonometry

AI Thread Summary
The discussion centers on the application of supplementary angles in spherical trigonometry, particularly in relation to dihedral angles and right spherical triangles. The user is confused about when to use acute versus obtuse angles while applying Napier's rules and seeks clarification on the conditions for angle selection. A specific problem involving a right spherical triangle is presented, where the user calculates angles and sides but questions the validity of supplementary values due to quadrant considerations. The user is also looking for additional resources and practice problems to enhance their understanding of spherical trigonometry. Overall, the thread highlights the complexities of angle relationships in spherical trigonometry and the need for clearer guidelines on their application.
jaycob1997
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I'm trying to review spherical trinometry on my own and I'm stuck where it says the supplement of the solved dihedral angle can be implemented. I'm using "PLANE AND SPHERICAL TRIGONOMETRY" by Paul Rider. Can anyone explain the concept behind that statement, because the examples that I have are quite confusing :confused:


Thanks!
 
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Let me just add some other information:

I'm using Napier's rules to solve for spherical angles and spherical sides for right spherical triangles. Now my problem is, when will I use the acute angles and not the supplement angles(Obtuse). Or are there any rule/s to follow on which angle to use.
 
Thanks for the link. Do you know other sites that I can go to regarding the same subject matter (Spherical Trigonometry), or if you know of any sites that have problems to solve so I can apply the concepts that I just learned. By the way, I'm self studying for my licensure examination, and a great deal of the exams comes from all fields of math.

Thanks again
 
I did further reading on the subject matter. This is where I got lost, the problem goes:

In a right spherical triangle (C=90 degrees), A=69 degrees and 50.8minutes, c=72 degrees and 15.4minutes, find B, a, b.

Using Napier's rules, I get

a=63 degrees and 23.8 minutes
b= 47 degrees7.0 minutes,
B=50 degrees and 17.7 minutes

a note is given at the end of the question stating that "The supplementary value is not admissible since 'A' (angle A) and 'a' (side a) do not terminate at the same quadrant" - but by inspection, the two values are both on the first quadrant. I'm totally lost :cry:
 
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