document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356839>Question 356839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a plane flies directly from New York to London and then to Nairobi and<BR>\n" );
document.write( "back to New York, it flies along the sides of a spherical triangle, as shown in Figure 11-28(a), approximately<BR>\n" );
document.write( "following the surface of Earth. On a sphere, the shortest path between two points is along an arc of a<BR>\n" );
document.write( "great circle. A great circle is obtained when a plane through the center of the sphere intersects the<BR>\n" );
document.write( "sphere. (An example of a great circle is the equator.) To obtain a great circle through two given points on<BR>\n" );
document.write( "the sphere, we need consider only a plane through the two points and the center of the sphere. A great<BR>\n" );
document.write( "circle through points A and B is shown in Figure 11-28(b). A spherical triangle consists of three points on<BR>\n" );
document.write( "the sphere and arcs of great circles (the shortest path) connecting the points.\r<BR>\n" );
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document.write( "a. How many great circles go through the North Pole and the South Pole on the globe?<BR>\n" );
document.write( "b. Describe a spherical triangle that has one vertex at the North Pole and the other two vertices on the<BR>\n" );
document.write( "equator.<BR>\n" );
document.write( "c. Is there a spherical triangle with three right angles? If so, find one. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254792 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=254792\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. How many great circles go through the North Pole and the South Pole on the globe?<BR>\n" );
document.write( "An infinite number.  Any plane that contains the line between the 2 poles intersects the sphere in a great circle.<BR>\n" );
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document.write( "b. Describe a spherical triangle that has one vertex at the North Pole and the other two vertices on the equator.<BR>\n" );
document.write( "The 2 angles on the equator are right angles.  The third can be from >zero to <180 degrees<BR>\n" );
document.write( "c. Is there a spherical triangle with three right angles? If so, find one.<BR>\n" );
document.write( "As in b above, if the angle at the pole is also 90 degs.<BR>\n" );
document.write( "For example, the pole, and longitude 0 degs and 90 degs on the equator.<BR>\n" );
document.write( " </SPAN>\n" );
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