Arc length in spherical triangle

Question

A spherical triangle has angles of 120◦, 60◦ and 45◦. Find the cosines of the (arc) lengths of the sides. How many sides have an arc length larger than 90◦?

Answer 1

you need to use the law of cosines, the one with the addition. If cosine is negative, it indicates that there is an obtuse angle which means the arc length will be larger than 90 in the number of angles.