document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120749>Question 1120749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In triangle ABC, AB=24m and angle ABC=90degree. Given that sin angle ACB=3/5, find<BR>\n" );
document.write( "I) the length of AC<BR>\n" );
document.write( "II) the length of BC<BR>\n" );
document.write( "III) the value of cos angle ACB+ tan angle BAC </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736430 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=736430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> triangle ABC is a right triangle with the right angle being at angle ABC.\r<BR>\n" );
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document.write( "AB = 24 meters.\r<BR>\n" );
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document.write( "sin(ACB) = 3/5.\r<BR>\n" );
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document.write( "since sine is opposite / hypotenuse, then sin(ACB) = 3/5 = 24/AC\r<BR>\n" );
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document.write( "since 3/5 = 24/AC, solve for AC to get AC = 24 * 5 / 3 = 40.\r<BR>\n" );
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document.write( "by pythagorus, [AB]^2 + [BC]^2 = [AC]^2 which becomes 24^2 + [BC]^2 = 40^2.\r<BR>\n" );
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document.write( "solve for BC to get BC = sqrt(40^2 - 24^2) = 32.\r<BR>\n" );
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document.write( "you have AB = 24, AC = 40, BC = 32.\r<BR>\n" );
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document.write( "cos(ACB) = adjacent / hypotenuse = BC/AC = 32/40\r<BR>\n" );
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document.write( "tan(BAC) = opposite / adjacent = BC / AB = 32/24\r<BR>\n" );
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document.write( "cos(ACB)) + tan(BAC) = 32/40 + 32/24 = 4/5 + 4/3 = 12/15 + 20/15 = 32/15.\r<BR>\n" );
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document.write( "that should be your answer.\r<BR>\n" );
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document.write( "solutions are:\r<BR>\n" );
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document.write( "AB = 24<BR>\n" );
document.write( "AC = 40<BR>\n" );
document.write( "BC = 32<BR>\n" );
document.write( "sin(ACB) + tan(BAC) = 32/15.\r<BR>\n" );
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document.write( "you could solve by finding the angles involved but that was unnecessary.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "sin(ACB) = 3/5 leads to angle ACB = 36.86989765.\r<BR>\n" );
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document.write( "since sum of angles of triangle is 180, then BAC = 180 - 90 - 36.86989765 = 53.13010235.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "angle ABC = 90<BR>\n" );
document.write( "angle ACB = 36.86989765<BR>\n" );
document.write( "angle BAC = 53.13010235.\r<BR>\n" );
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document.write( "sin(ACB)) = c/b becomes sin(36.8689765) = 24/b\r<BR>\n" );
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document.write( "solve for b to get b = 24/sin(36.8689765) = 40\r<BR>\n" );
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document.write( "cos(ACB) = a/b bcomes cos(36.8689765) = a/40\r<BR>\n" );
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document.write( "solve for a to get a = 40 * cos(36.8689765) = 32.\r<BR>\n" );
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document.write( "cos(ACB) + tan(BAC) = cos(36.86989765 + tan(53.13010235) = 2.133333333....\r<BR>\n" );
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document.write( "the denominator is assumed to be 1.\r<BR>\n" );
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document.write( "multiply numerator and denominator of that by 15 and it becomes 32/15.\r<BR>\n" );
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document.write( "that'as the same answer i got earlier.\r<BR>\n" );
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document.write( "all answser check out.\r<BR>\n" );
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document.write( "your solutions are:\r<BR>\n" );
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document.write( "AC = 40<BR>\n" );
document.write( "BC = 32<BR>\n" );
document.write( "cos(ACB) + tan(BAC) = 32/15 = 2.3333333333......\r<BR>\n" );
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document.write( "my diagram is shown below.\r<BR>\n" );
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document.write( "in the diagram:\r<BR>\n" );
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document.write( "c is the same as AB<BR>\n" );
document.write( "b is the same as AC<BR>\n" );
document.write( "a is the same as BC.\r<BR>\n" );
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document.write( "angles shown are rounded to 1 decimal point, but calculations are made from the maximum number of decimal points for each as stored in the calculator.\r<BR>\n" );
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