# Finding the sides of a right spherical triangle

I need some help with spherical triangles. I am looking for the lengths of the sides of a spherical triangle given that all the angles. One being 90 degrees and the other 2 angles being 50 and 70 degrees. I don't even know how to go about solving this. I know there are 4 formulas for solving these tyle of problems the sine formula, the cosine formula, the polar cosine formula, and the cotangent formula. I also saw something called Napiers formula where you might use a pentagon to show the relationship of angles to sides so maybe I can find an answer with that. I have no idea where to begin to sove this, nor can I find a single example to follow. Please Help!

## Answers and Replies

sas3
Gold Member
Look up Girard's theorem that should help you.

Thanks so much for a response!

Girards formula gives me formulas for the area of a spherical triangle. Do I have to find the area in order to find the length of the sides? Do you know where I can see examples of solved problems like this. I can't find a single one.

sas3
Gold Member
Sorry, for some reason I was thinking area and not radian arc length, what you are looking for is the “Haversine formula”

I think you will find some examples in Wiki.

So the Haversine formula states that cos(c) = cos(a)cos(b) + sin(a)sin(b)sin(C)

I for all of this formula all I really know is C for each formula. So if I have 50 degrees, do I write that the side opposite of that is:

cos(50) = (cos(a)cos(b) - cos(c))/(sin(a)sin(b))

I don't see how I can figure it out anymore than that not knowing what a b or c is? I'm so lost with this stuff!