Trigonometry

What is the spherical excess of a spherical triangle whose angles are all right angles?

The area of spherical triangle ABC whose parts are \(A=93^\circ 40'\), \(B=64^\circ 12'\), \(C=116^\circ 51'\) and the radius of the sphere is 100 m is

A spherical triangle has an area of 327.25 sq. km. What is the radius of the sphere if its spherical excess is 30°?

A ship on a certain day is at latitude \(20^\circ\) N and longitude \(140^\circ\) E. After sailing for 150 hours at a uniform speed along a great circle route, it reaches a point at latitude \(10^\circ S\) and longitude \(170^\circ\) E. If the radius of the earth is 3959 miles, find the speed in miles per hour.