document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126582>Question 1126582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find all solutions to the following triangle. (Round your answers for the angles B, C, B', and C' to the nearest whole number. Round your answers for the sides c and c' to one decimal place. If either triangle is not possible, enter NONE in each corresponding answer blank.)<BR>\n" );
document.write( "A = 65°, b = 6.7 yd, a = 6.2 yd<BR>\n" );
document.write( "First triangle (assume B &#8804; 90°):<BR>\n" );
document.write( "B= 	     °<BR>\n" );
document.write( "C= 	     °<BR>\n" );
document.write( "c = 	     yd<BR>\n" );
document.write( "Second triangle (assume B' > 90°):<BR>\n" );
document.write( "B'= 	     °<BR>\n" );
document.write( "C'= 	     °<BR>\n" );
document.write( "c'= 	     yd<BR>\n" );
document.write( " </SPAN>\n" );
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document.write( "In this kind of problem, you are always given one angle and the length of the side opposite that angle, plus the length of one of the two other sides.<br><BR>\n" );
document.write( "I find it easiest always to draw the figure in the same orientation: unknown side horizontal, with the given angle at the left.<br><BR>\n" );
document.write( "So in this problem the horizontal base is AB, with the 65 degree angle A at the left.  Side b slants up to the right from A to C; side a slants down from C to B.<br><BR>\n" );
document.write( "The height of the triangle (vertical distance from C to side AB) is b*sinA() = 6.7*sin(65) = 6.07.  Since side a is greater than 6.07 and less than 6.7, there will be two triangles.<br><BR>\n" );
document.write( "The required calculations are then....<br><BR>\n" );
document.write( "(1) Find the measure of the acute angle B using the law of sines.<BR>\n" );
document.write( "(2) By symmetry, the obtuse angle B will be 180 degrees minus the acute angle B.<BR>\n" );
document.write( "(3) Find angle C of each triangle using the angle sum of 180 degrees for a triangle.<BR>\n" );
document.write( "(4) Find the lengths of side c in each triangle using the law of sines. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );