document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=956339>Question 956339</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having some trouble with Algebra 2. The problem is:\r<BR>\n" );
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document.write( "Find the area of ABC.\r<BR>\n" );
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document.write( "(A) = 50° ; AB = 15; and AC = 10   Area =\r<BR>\n" );
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document.write( "(B) = 75° ; CB = 12 ; and AB = 16   Area =\r<BR>\n" );
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document.write( "I know the Pythagorean Theorem is A^2 + B^2 = C^2, but I'm unsure how to use it in this case. <BR>\n" );
document.write( "What I did so far for A is add 15^2 (225) and 10^2 (100) to get 325. Am I doing it right?\r<BR>\n" );
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document.write( "Thanks for the help, I appreciate it!\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #584258 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=584258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the area of ABC.\r<BR>\n" );
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document.write( "(A) = 50° ; AB = 15; and AC = 10 Area =\r<BR>\n" );
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document.write( "(B) = 75° ; CB = 12 ; and AB = 16 Area =\r<BR>\n" );
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document.write( "The area of a triangle is equal to 1/2 * the base * the height.\r<BR>\n" );
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document.write( "if you let b = the base and h = the height, and a equal the area, then the formula becomes:\r<BR>\n" );
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document.write( "a = 1/2 * b * h\r<BR>\n" );
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document.write( "you are not given the height so you have to find it.\r<BR>\n" );
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document.write( "you also need to re-orient your triangles so that the given angle is not opposite the base of the triangle.\r<BR>\n" );
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document.write( "this will allow you to solve for h easily.\r<BR>\n" );
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document.write( "in the first triangle, make A bottom left and B top middle and C bottom right and then draw h from B intersecting with AC at D forming a 90 degree angle with AC.   This makes h the height of the triangle and it makes AC the base of the triangle.\r<BR>\n" );
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document.write( "in the second triangle, make C bottom left and A middle top and B bottom right and then draw h from A intersecting with CB at D forming a 90 degree angle with CB.  This makes h the height of the triangle and it makes CB the base of the triangle.\r<BR>\n" );
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document.write( "Now you are ready to solve.\r<BR>\n" );
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document.write( "First you need to find h.\r<BR>\n" );
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document.write( "In the first triangle, sin(50) = opp/hyp = h/15.<BR>\n" );
document.write( "solve for h to get h = 15 * sin(50).\r<BR>\n" );
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document.write( "In the second triangle, sin(75) = opp/hyp = h/16.<BR>\n" );
document.write( "solve for h to get h = 16 * sin(75).\r<BR>\n" );
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document.write( "the formula for the area of a triangle is a = 1/2 * b * h\r<BR>\n" );
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document.write( "a is the area.<BR>\n" );
document.write( "b is the base.<BR>\n" );
document.write( "h is the height.\r<BR>\n" );
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document.write( "in the first triangle, you get:\r<BR>\n" );
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document.write( "a = 1/2 * b * h becomes:\r<BR>\n" );
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document.write( "a = 1/2 * 10 * 15 * sin(50).\r<BR>\n" );
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document.write( "in the second triangle, you get:\r<BR>\n" );
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document.write( "a = 1/2 * b * h becomes:\r<BR>\n" );
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document.write( "a = 1/2 * 12 * 16 * sin(75).\r<BR>\n" );
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document.write( "use your calculator to solve:\r<BR>\n" );
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document.write( "in the first triangle you get a = 57.45 square units.\r<BR>\n" );
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document.write( "in the second triangle you get a = 92.73 square units.\r<BR>\n" );
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document.write( "results are rounded to 2 decimal places.\r<BR>\n" );
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document.write( "a picture of your triangles is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/031702.jpg\" alt = \"$$$\" </><BR>\n" );
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