# problem or doubt regarding visualizing angles of spherical triangle

I must confess that I am not able to visualize or understand what is the angle of a spherical triangle say $ABC$ where $A,B,C$ are vertices of the triangle which is formed by intersection of three great circle, and say $a,b,c$ are sides (which are arc on the sphere) of the triangle, what is meant by right spherical triangle say if some one says angle at $C$ is $90$ degree, is it possible to have more than one angle $90$ degree in a spherical triangle I know one result that sum of angles of a spherical triangle is $a+b+c-\pi$, if the radius of the sphere is $r$ then what is the relation between $a,b,c$ with $r$ if there is any. advanced Thank you for clearing my doubts with a picture.

• A spherical triangle can have three right-angles. – A. Chu Mar 17 '13 at 7:50
• Get an orange and slice it into 8 pieces, by cutting in planes through the center. Stare at the pieces. – bubba Mar 17 '13 at 8:31
• what about sides?how to define or find their length? – miosaki Mar 18 '13 at 4:54

Here's a picture of a spherical triangle with three right angles. It consists of $1/4$ of the equator and half of two meridians at longitudes $0$ and $\pi/2$.