document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146878>Question 1146878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a right triangle, the length of one of the legs is 8 cm and the measure of the acute angle opposite to this leg is 50°. Find the measure of the other acute angle and the lengths of the other leg and the hypotenuse. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #768170 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=768170\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can use the law of sines to solve this.<BR>\n" );
document.write( "law of sines says a/sin(A) = b/sin(B) = c/sin(C)<BR>\n" );
document.write( "let your triangle be ABC<BR>\n" );
document.write( "A is the 90 degree angle.<BR>\n" );
document.write( "B is the 40 degree angle.<BR>\n" );
document.write( "C is the 50 degree angle.<BR>\n" );
document.write( "a is the side opposite angle (A)<BR>\n" );
document.write( "b is the side opposite angle (B) <BR>\n" );
document.write( "c is the side opposite angle (C)<BR>\n" );
document.write( "measure of side c is 8.<BR>\n" );
document.write( "measure of angle (C) is 50 degrees.<BR>\n" );
document.write( "since angle A is 90 degrees, then angle B has to be 180 - 90 - 50 = 40 degrees.<BR>\n" );
document.write( "law of sines says a/sin(A) = c/sin(C)<BR>\n" );
document.write( "c = 8 and C = 50 and A = 90<BR>\n" );
document.write( "formula becomes:<BR>\n" );
document.write( "a/sin(90) = 8/sin(50)<BR>\n" );
document.write( "solve for a to get:<BR>\n" );
document.write( "a = 8 * sin(90) / sin(50) = 10.44325831<BR>\n" );
document.write( "likewise, .....<BR>\n" );
document.write( "c/sin(C) = b/sin(B)<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "8/sin(50) = b/sin(40)<BR>\n" );
document.write( "solve for b to get:<BR>\n" );
document.write( "b = 8 * sin(40) / sin(50) = 6.712797049<BR>\n" );
document.write( "this is a right triangle where:<BR>\n" );
document.write( "the two legs are c and b, and he hypotenuse is a.<BR>\n" );
document.write( "your leg measurements are:<BR>\n" );
document.write( "c = 8<BR>\n" );
document.write( "b = 6.712797049<BR>\n" );
document.write( "the hypotenuse measurement is:<BR>\n" );
document.write( "c = 10.44325831<BR>\n" );
document.write( "in a right triangle, the sum of the square of each leg is equal to the square of the hypotenuse.<BR>\n" );
document.write( "that means that 6.712797049^2 + 8^2 = 10.44325831^2<BR>\n" );
document.write( "do the math and you will see that 109.0616442 = 109.0616442, confirming that the lengths of the legs and the hypotenuse are correct.<BR>\n" );
document.write( "your solution is:<BR>\n" );
document.write( "the other acute angle is 40 degrees.<BR>\n" );
document.write( "the length of the other leg is 6.712797049<BR>\n" );
document.write( "the length of the hypotenuse is 10.44325831<BR>\n" );
document.write( "here's my diagram.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/101302.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );