document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919179>Question 919179</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two sides an angle of a triangle are given, determine whether the given measurements produce one triangle, two triangles or no triangle at all.\r<BR>\n" );
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document.write( "a = 10 b = 9 A = 30 degrees\r<BR>\n" );
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document.write( "(Im very stuck on this problem and the choices they give us is like B = what or C = and also C1 and B1 etc.\r<BR>\n" );
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document.write( "please help!\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557537 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=557537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I don't know how to draw on line, so bear with me!<BR>\n" );
document.write( "Draw a horizontal line 10 units long and label it AC, this is your line a.<BR>\n" );
document.write( "Use your protractor to draw a line 30 degrees above and about point A. This is angle A = 30. Now measure 9 units along that 30 degree line and label the end point as B. This line AB is your line b = 9. Now draw a line to join point B and point C on line AC. This line is c. Got the triangle? Hope so.<BR>\n" );
document.write( "Now you need to do some trig to find B, C and c.<BR>\n" );
document.write( "To do this, drop a line from point B down to and perpendicular to line AC. Label the point of intersection M, and label the line as h. Now you have a right triangle ABM, where AB = 9 and A = 30 degrees. Label the line AM as x. then we have<BR>\n" );
document.write( "(1) cos(A) = x/9 or<BR>\n" );
document.write( "(2) x = 9*cos(A) or<BR>\n" );
document.write( "(3) x = 9*cos(30) or<BR>\n" );
document.write( "In the same triangle we have<BR>\n" );
document.write( "(4) sin(A) = h/9 or<BR>\n" );
document.write( "(5) h = 9*sin(30) or<BR>\n" );
document.write( "(6) h = 4.5 (this is exact because sin(30) = 1/2)<BR>\n" );
document.write( "So far so good.<BR>\n" );
document.write( "Look at your triangle and label the line MC as y. Note that<BR>\n" );
document.write( "(7) x + y = a = 10 or<BR>\n" );
document.write( "(8) y = 10 - x or<BR>\n" );
document.write( "(9) y = 10 - 9*cos(30)<BR>\n" );
document.write( "Also note that <BR>\n" );
document.write( "(10) tan(C) = h/y or<BR>\n" );
document.write( "(11) tan(C) = 4.5/(10 - 9*cos(30)) or<BR>\n" );
document.write( "(12) C = arctan(4.5/(10 - 9*cos(30)))<BR>\n" );
document.write( "Use your calculator to find<BR>\n" );
document.write( "(13) angle C is approx 63.887... degrees.<BR>\n" );
document.write( "Using the identity<BR>\n" );
document.write( "(14) A+B+C = 180 we have<BR>\n" );
document.write( "(15) 30 + B + 63.887... = 180 or<BR>\n" );
document.write( "(16) angle B is approx 86.113... degrees.<BR>\n" );
document.write( "Lastly we need c. We can use<BR>\n" );
document.write( "(17) sin(C) = h/c or<BR>\n" );
document.write( "(18) c = 4.5/sin(C)<BR>\n" );
document.write( "Using your calculator and C of (12) we get<BR>\n" );
document.write( "(19) line c is approx 5.0115<BR>\n" );
document.write( "We can check c using<BR>\n" );
document.write( "(20) c^2 = y^2 + h^2 or<BR>\n" );
document.write( "Is (5.0115^2 = 2.20577^2 + 4.5^2)?<BR>\n" );
document.write( "Is (5.0115^2 = 4.8654... + 20.25)?<BR>\n" );
document.write( "Is (5.0115^2 = 25.1154...)?<BR>\n" );
document.write( "Is (5.0115^2 = 5.0115^2)? Yes<BR>\n" );
document.write( "Answer: The given values form a single scalene triangle ABC, whose sides are a=10, b=9 and c=5.0115... with anles A = 30, B = 86.113... and C = 63.887... degrees.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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