document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202430>Question 1202430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sketch q figure and solve each right triangle ABC with right angle at C.<BR>\n" );
document.write( "1. A = 76° and a = 13<BR>\n" );
document.write( "2. A = 22° and b = 22<BR>\n" );
document.write( "3. B = 30° and b = 11<BR>\n" );
document.write( "4. B = 18° and a = 18<BR>\n" );
document.write( "5. A = 77° and b = 42<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 #837275 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837275\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll do problem 1 to get you started.\r<BR>\n" );
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document.write( "The phrasing \"solve the triangle\" means \"find the missing sides and missing angles\".\r<BR>\n" );
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document.write( "Side a is opposite angle A.<BR>\n" );
document.write( "Side b is opposite angle B.<BR>\n" );
document.write( "Side c is opposite angle C.\r<BR>\n" );
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document.write( "The right angle, aka 90 degree angle, is at C<BR>\n" );
document.write( "C = 90<BR>\n" );
document.write( "We denote this with a square angle marker as shown in the diagrams below.\r<BR>\n" );
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document.write( "Angles A and B are complementary. They add to 90<BR>\n" );
document.write( "A+B = 90<BR>\n" );
document.write( "76+B = 90<BR>\n" );
document.write( "B = 90-76<BR>\n" );
document.write( "B = 14\r<BR>\n" );
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document.write( "Or we could say:<BR>\n" );
document.write( "A+B+C = 180<BR>\n" );
document.write( "76+B+90 = 180<BR>\n" );
document.write( "166+B = 180<BR>\n" );
document.write( "B = 180-166<BR>\n" );
document.write( "B = 14\r<BR>\n" );
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document.write( "This is what we have so far<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Aline%28-3%2C-3%2C3%2C-3%29%2C%0D%0Aline%283%2C-3%2C3%2C3%29%2C%0D%0Aline%283%2C3%2C-3%2C-3%29%2C%0D%0Aline%283-0.5%2C-3%2C3-0.5%2C-3%2B0.5%29%2C%0D%0Aline%283-0.5%2C-3%2B0.5%2C3%2C-3%2B0.5%29%2C%0D%0A%0D%0Acircle%28-3%2C-3%2C0.04%29%2C%0D%0Acircle%28-3%2C-3%2C0.06%29%2C%0D%0Acircle%28-3%2C-3%2C0.08%29%2C%0D%0Acircle%28-3%2C-3%2C0.10%29%2C%0D%0A%0D%0Acircle%283%2C-3%2C0.04%29%2C%0D%0Acircle%283%2C-3%2C0.06%29%2C%0D%0Acircle%283%2C-3%2C0.08%29%2C%0D%0Acircle%283%2C-3%2C0.10%29%2C%0D%0A%0D%0Acircle%283%2C3%2C0.04%29%2C%0D%0Acircle%283%2C3%2C0.06%29%2C%0D%0Acircle%283%2C3%2C0.08%29%2C%0D%0Acircle%283%2C3%2C0.10%29%2C%0D%0A%0D%0Alocate%283%2B0.1%2C0%2C%22a=13%22%29%2C%0D%0Alocate%28-0.3%2C-3-0.1%2C%22b%22%29%2C%0D%0Alocate%28-0.4%2C0.4%2C%22c%22%29%2C%0D%0A%0D%0Alocate%28-3-0.4%2C-3%2B0.2%2C%22A%22%29%2C%0D%0Alocate%283%2B0.2%2C3%2B0.2%2C%22B%22%29%2C%0D%0Alocate%283%2B0.2%2C-3%2B0.2%2C%22C%22%29%2C%0D%0A%0D%0Alocate%28-3%2B0.5%2C-3%2B0.65%2C76%5Eo%29%2C%0D%0Alocate%283-0.65%2C3-0.5%2C14%5Eo%29%2C%0D%0A%0D%0Alocate%28-4.5%2C-4%2Cmatrix%281%2C2%2C%22Diagram%22%2C%22not%22%29%29%2C%0D%0Alocate%28-4.5%2C-4.5%2Cmatrix%281%2C2%2C%22to%22%2C%22scale%22%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We'll use the soh cah toa trig ratios to fill in the missing sides.<BR>\n" );
document.write( "soh = sine opposite hypotenuse<BR>\n" );
document.write( "cah = cosine adjacent hypotenuse<BR>\n" );
document.write( "toa = tangent opposite adjacent\r<BR>\n" );
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document.write( "Here is one way to find side c.<BR>\n" );
document.write( "sin(angle) = opposite/hypotenuse<BR>\n" );
document.write( "sin(A) = a/c<BR>\n" );
document.write( "sin(76) = 13/c<BR>\n" );
document.write( "c*sin(76) = 13<BR>\n" );
document.write( "c = 13/sin(76)<BR>\n" );
document.write( "c = 13.39797718<BR>\n" );
document.write( "c = 13.398 which is approximate<BR>\n" );
document.write( "Make sure your calculator is in degree mode.<BR>\n" );
document.write( "I'll let the student explore the 2nd pathway to determine c (hint: cos(B) = a/c).\r<BR>\n" );
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document.write( "Let's find side b.<BR>\n" );
document.write( "sin(angle) = opposite/hypotenuse<BR>\n" );
document.write( "sin(B) = b/c<BR>\n" );
document.write( "sin(14) = b/13.39797718<BR>\n" );
document.write( "b = 13.39797718*sin(14)<BR>\n" );
document.write( "b = 3.24126404<BR>\n" );
document.write( "b = 3.241<BR>\n" );
document.write( "There are three more pathways using a trig ratio, which I'll let the student explore further (hints: cos(A) = b/c, tan(A) = a/b, and tan(B) = b/a)\r<BR>\n" );
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document.write( "Or we could use the pythagorean theorem<BR>\n" );
document.write( "a^2+b^2 = c^2<BR>\n" );
document.write( "13^2 + b^2 = (13.39797718)^2<BR>\n" );
document.write( "169 + b^2 = 179.5057925158<BR>\n" );
document.write( "b^2 = 179.5057925158 - 169<BR>\n" );
document.write( "b^2 = 10.5057925158<BR>\n" );
document.write( "b = sqrt(10.5057925158)<BR>\n" );
document.write( "b = 3.24126403055969<BR>\n" );
document.write( "b = 3.241\r<BR>\n" );
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document.write( "Here's the completed right triangle with all angles and all sides labeled. The decimal values are approximate. Round however your teacher instructs.<BR>\n" );
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