document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036322>Question 1036322</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One acute angle of a right triangle is not less than 30° more than twice the other acute angle. What are the possible measures of the larger angle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650990 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=650990\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the 2 acute angles of the right triangle be represented by a and b.<BR>\n" );
document.write( "you get a + b = 90.<BR>\n" );
document.write( "if a is not less than 2b + 30, then a must be greater than or equal to 2b + 30.<BR>\n" );
document.write( "your equation is therefore a >= 2b + 30<BR>\n" );
document.write( "since a + b = 90, then b = 90 - a and the equation becomes a >= 2 * (90 - a) + 30.<BR>\n" );
document.write( "simplify this is to get a >= 180 - 2a + 30.<BR>\n" );
document.write( "add 2a to both sides of the equation and combine like terms to get 3a >= 210.<BR>\n" );
document.write( "divide both sides of this equation by 3 to get a >= 70.<BR>\n" );
document.write( "if a >= 70, then b <= 20 because a + b = 90.<BR>\n" );
document.write( "let's see how this works.<BR>\n" );
document.write( "let's assume that a = 70.<BR>\n" );
document.write( "this means that b = 20 and we get 2 * 20 + 30 = 70.<BR>\n" );
document.write( "this satisfies the requirement that a is not less than 2 * b + 30 because a = 2 * b + 30, so we're good.<BR>\n" );
document.write( "now let's look at a = 71 degrees.<BR>\n" );
document.write( "this means that b = 19 degrees.<BR>\n" );
document.write( "a >= 2 * b + 30 means 71 >= 2 * 19 + 30 which means that 71 >= 68.<BR>\n" );
document.write( "this means that a is not less than 2 * b + 30 because a is greater than 2 * 19 + 30.<BR>\n" );
document.write( "looks like the requirements of the problem are satisfied.<BR>\n" );
document.write( "take any angle greater than or equal to 70 but less than or equal to 90 and the requirements of the problem will be satisfied.<BR>\n" );
document.write( "lets take one look at a smaler than 70.<BR>\n" );
document.write( "assume a = 69.<BR>\n" );
document.write( "this makes b = 21.<BR>\n" );
document.write( "2*b + 30 is equal to 42 + 30 = 72.<BR>\n" );
document.write( "in this case a < 2 * b +30 because 69 is smaller than 72, so we're not good since a is not greater than or equal to 70.<BR>\n" );
document.write( "the requirements are only satisfied when a is >= 70.<BR>\n" );
document.write( "your solution is that the possible measures of the larger angle are 70 <= a <= 90, where a represents the larger angle.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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