document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099331>Question 1099331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "Please help me solve this question.\r<BR>\n" );
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document.write( "a is an acute angle such that sin a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F%282%2Asqrt%286%29%29+ ALIGN=MIDDLE  ALT=\"+3%2F%282%2Asqrt%286%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By sketching a right angled triangle, show that tan a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2Fsqrt%2815%29+ ALIGN=MIDDLE  ALT=\"+3%2Fsqrt%2815%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "How do I do this when I don't have a side length to work out the angle with trigonometry? Please help me! I'm so confused. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #713779 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=713779\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The word \"sketch\" suggests that you would just draw something as an illustration,<BR>\n" );
document.write( "without caring for accuracy or straightness of the lines,<BR>\n" );
document.write( "maybe labeling vertices,<BR>\n" );
document.write( "and based on the drawing would use your knowledge of trigonometry,<BR>\n" );
document.write( "and of the Pythagorean theorem to calculate<BR>\n" );
document.write( "what the values of the trigonometric ratio would be<BR>\n" );
document.write( "for an ideal triangle where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=3%2F%282%2Asqrt%286%29%29+ ALIGN=MIDDLE  ALT=\"sin%28A%29=3%2F%282%2Asqrt%286%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > exactly.<BR>\n" );
document.write( "It could be something like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C240%2C-0.5%2C4.5%2C-0.5%2C3.5%2C%0D%0Atriangle%280%2C0%2C4%2C0%2C0%2C3%29%2Crectangle%280%2C0%2C0.2%2C0.2%29%2C%0D%0Alocate%284.1%2C0.2%2CA%29%2Clocate%28-0.1%2C3.3%2CB%29%2C%0D%0Alocate%28-0.1%2C0%2CC%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The angles of that drawing are not such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=3%2F%282%2Asqrt%286%29%29+ ALIGN=MIDDLE  ALT=\"sin%28A%29=3%2F%282%2Asqrt%286%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but we say it is just a \"sketch\" representing the problem.<BR>\n" );
document.write( "Then you could say that your triangle has BC and AB side lengths<BR>\n" );
document.write( "(no need to mentions units or measure sides)<BR>\n" );
document.write( "that yield <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=3%2F%282%2Asqrt%286%29%29+ ALIGN=MIDDLE  ALT=\"sin%28A%29=3%2F%282%2Asqrt%286%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "such as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=2%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"AB=2%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=3 ALIGN=MIDDLE  ALT=\"BC=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "With the numbers above, you could calculate AC.<BR>\n" );
document.write( "The Pythagorean theorem says that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC%5E2%2BBC%5E2%2BAB%5E2 ALIGN=MIDDLE  ALT=\"AC%5E2%2BBC%5E2%2BAB%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC%5E2%2B3%5E2=%282%2Asqrt%286%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"AC%5E2%2B3%5E2=%282%2Asqrt%286%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC%5E2%2B9=2%5E2%2A%28sqrt%286%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"AC%5E2%2B9=2%5E2%2A%28sqrt%286%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC%5E2%2B9=4%2A6 ALIGN=MIDDLE  ALT=\"AC%5E2%2B9=4%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC%5E2%2B9=24 ALIGN=MIDDLE  ALT=\"AC%5E2%2B9=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC%5E2=24-9 ALIGN=MIDDLE  ALT=\"AC%5E2=24-9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC%5E2=15 ALIGN=MIDDLE  ALT=\"AC%5E2=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=sqrt%2815%29 ALIGN=MIDDLE  ALT=\"AC=sqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28A%29=BC%2FAC=3%2Fsqrt%2815%29 ALIGN=MIDDLE  ALT=\"tan%28A%29=BC%2FAC=3%2Fsqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "You could also just state that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=BC%2FAB=3%2F%282%2Asqrt%286%29%29 ALIGN=MIDDLE  ALT=\"sin%28A%29=BC%2FAB=3%2F%282%2Asqrt%286%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and work the same calculations without specific length.<BR>\n" );
document.write( "It just gets to be more cumbersome.<BR>\n" );
document.write( " <BR>\n" );
document.write( "There is an infinite number of similar right triangles that have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=3%2F%282%2Asqrt%286%29%29+ ALIGN=MIDDLE  ALT=\"sin%28A%29=3%2F%282%2Asqrt%286%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "They all look like scaled up or scale down versions of one another, and they all have the same <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28A%29=3%2Fsqrt%2815%29+ ALIGN=MIDDLE  ALT=\"tan%28A%29=3%2Fsqrt%2815%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Saying that the one you sketched has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=2%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"AB=2%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=3 ALIGN=MIDDLE  ALT=\"BC=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is good enough for a proof in my book.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The wording of the question sounds like you are expected to draw a right triangle ABC<BR>\n" );
document.write( "such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=3%2F%282%2Asqrt%286%29%29+ ALIGN=MIDDLE  ALT=\"sin%28A%29=3%2F%282%2Asqrt%286%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "measure its legs, and calculate the tangent of A as a ratio of leg lengths.<BR>\n" );
document.write( "I do not hink that is what was meant.<BR>\n" );
document.write( "Doing an exact drawing without using the fact that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28A%29=3%2Fsqrt%2815%29+ ALIGN=MIDDLE  ALT=\"tan%28A%29=3%2Fsqrt%2815%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  is a bit tricky,<BR>\n" );
document.write( "but I will show you what your knowledge of geometry can do for you.<BR>\n" );
document.write( "First you must decide how large to make your triangle.<BR>\n" );
document.write( "There is an infinite number of similar right triangles that have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29=3%2F%282%2Asqrt%286%29%29+ ALIGN=MIDDLE  ALT=\"sin%28A%29=3%2F%282%2Asqrt%286%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "They all look like scaled up or scale down versions of one another, and they all have the same <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28A%29=3%2Fsqrt%2815%29+ ALIGN=MIDDLE  ALT=\"tan%28A%29=3%2Fsqrt%2815%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Let's say you deice that the hypotenuse of your right triangle will measure 100mm.<BR>\n" );
document.write( "Draw a line, set your compass for a circle of radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2F2=50mm ALIGN=MIDDLE  ALT=\"AB%2F2=50mm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and draw an arc that crosses your line at two points, A and B, like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C175%2C-60%2C60%2C-60%2C10%2C%0D%0Aline%28-60%2C0%2C60%2C0%29%2Carc%280%2C0%2C100%2C100%2C-10%2C190%29%2C%0D%0Alocate%2852%2C6%2CA%29%2Clocate%28-54%2C6%2CB%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Now, set the compass for an arc of radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100mm%29%2A%283%2F%282%2Asqrt%286%29%29%29=61.2mm ALIGN=MIDDLE  ALT=\"%28100mm%29%2A%283%2F%282%2Asqrt%286%29%29%29=61.2mm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and draw a small arc centered at B that crosses the arc you made before.<BR>\n" );
document.write( "The point where the arcs cross is point C, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=AB%2Asin%28A%29 ALIGN=MIDDLE  ALT=\"BC=AB%2Asin%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C175%2C-60%2C60%2C-60%2C10%2C%0D%0Aline%28-60%2C0%2C60%2C0%29%2Carc%280%2C0%2C100%2C100%2C-10%2C190%29%2C%0D%0Alocate%2852%2C6%2CA%29%2Clocate%28-54%2C6%2CB%29%2C%0D%0Aarc%28-50%2C0%2C122.4%2C122.4%2C45%2C60%29%2C%0D%0Alocate%28-13%2C-49%2CC%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Connect point C to points A and B to get your right triangle.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The reason this works is because<BR>\n" );
document.write( "1) an inscribed angle that intercepts a semicircle is always a right angle, and<BR>\n" );
document.write( "2)we made AB and BC such that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%2FAB ALIGN=MIDDLE  ALT=\"BC%2FAB\"   DISABLED_style= \"max-width:90%; height:auto;\" > was the value we needed for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28A%29 ALIGN=MIDDLE  ALT=\"sin%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );