# Finding the sides of a right spherical triangle

• lilcoley23@ho
In summary, the conversation discusses the need for help with spherical triangles and the various formulas that can be used to solve problems involving the lengths of sides and angles. The Haversine formula is mentioned as a potential solution, but the individual is unsure how to use it without knowing the values of a, b, and c. They also express frustration in finding examples to follow.
lilcoley23@ho
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!

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.

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!

## 1. How do you define a right spherical triangle?

A right spherical triangle is a triangle formed on the surface of a sphere, where one of the angles measures 90 degrees.

## 2. What are the three sides of a right spherical triangle called?

The three sides of a right spherical triangle are called the hypotenuse, the opposite, and the adjacent.

## 3. How do you find the length of the sides of a right spherical triangle?

The length of the sides of a right spherical triangle can be found using the cosine, sine, and tangent functions, as well as the radius of the sphere and the given angles.

## 4. Is the Pythagorean theorem valid for right spherical triangles?

Yes, the Pythagorean theorem can be used to find the length of the sides of a right spherical triangle, just like it is used for right triangles in Euclidean geometry.

## 5. Can a right spherical triangle have multiple solutions?

Yes, a right spherical triangle can have multiple solutions, as there can be more than one set of angles and sides that satisfy the given conditions.

Replies
5
Views
1K
Replies
9
Views
2K
Replies
1
Views
1K
Replies
6
Views
865
Replies
8
Views
3K
Replies
2
Views
883
Replies
1
Views
3K
Replies
2
Views
1K
Replies
4
Views
11K
Replies
3
Views
350