In this research we study the spherical and right angle spherical triangle of the elliptic geometry and study the history of elliptic geometry, and define the geodesic and spherical and polar triangles, and at the end we study the spherical trigonometerical relations. The study aimed to: explain some of the spherical triangles applications on other sciences. determine the location of star in the space, find the horizontal angle of the correspondent oblique angle. find the angle of landing and embarkation of the airplane and calculate the time the airplane spend on route between tow destinations on the glob surface.