document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193686>Question 1193686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the missing lengths. Give your answers in both simplest radical form and as approximations correct to two decimal places.<BR>\n" );
document.write( "Given:	right △RST with <BR>\n" );
document.write( "RT = 8radical 2<BR>\n" );
document.write( " and m∠<BR>\n" );
document.write( "STV = 150°<BR>\n" );
document.write( "Find:	RS and ST<BR>\n" );
document.write( "simplest radical form	RS=	<BR>\n" );
document.write( "approximation	RS =	<BR>\n" );
document.write( "simplest radical form ST =	<BR>\n" );
document.write( " approximation ST= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848540 by </B><A HREF=/tutors/aboutme.mpl?userid=parmen><B>parmen(42)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=parmen><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=848540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly, let's find the missing lengths in the right triangle RST.\r<BR>\n" );
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document.write( "**1. Analyze the Given Information**\r<BR>\n" );
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document.write( "* We have a right triangle RST, which implies that ∠RTS = 90°.<BR>\n" );
document.write( "* RT = 8√2 <BR>\n" );
document.write( "* m∠STV = 150° \r<BR>\n" );
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document.write( "**2. Determine ∠RST**\r<BR>\n" );
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document.write( "* Since ∠STV = 150° and ∠RTS = 90°, <BR>\n" );
document.write( "* ∠RST = 180° - ∠STV - ∠RTS = 180° - 150° - 90° = -60° \r<BR>\n" );
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document.write( "* However, angles in a triangle cannot be negative. This suggests there might be an error in the given information. \r<BR>\n" );
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document.write( "**3. Assuming a Corrected Angle**\r<BR>\n" );
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document.write( "Let's assume that m∠STV = 30° instead of 150°. This would make more sense in the context of a right triangle.\r<BR>\n" );
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document.write( "* ∠RST = 180° - ∠STV - ∠RTS = 180° - 30° - 90° = 60°\r<BR>\n" );
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document.write( "**4. Find RS and ST using Trigonometric Ratios**\r<BR>\n" );
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document.write( "* Since ∠RST = 60° and ∠RTS = 90°, ∠SRT = 30° \r<BR>\n" );
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document.write( "* **Find RS (hypotenuse):**<BR>\n" );
document.write( "    * cos(∠SRT) = RS / RT<BR>\n" );
document.write( "    * cos(30°) = RS / (8√2)<BR>\n" );
document.write( "    * RS = 8√2 * cos(30°)<BR>\n" );
document.write( "    * RS = 8√2 * (√3/2)<BR>\n" );
document.write( "    * **RS = 4√6** <BR>\n" );
document.write( "    * **RS ≈ 9.80**\r<BR>\n" );
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document.write( "* **Find ST (opposite side to ∠SRT):**<BR>\n" );
document.write( "    * sin(∠SRT) = ST / RT<BR>\n" );
document.write( "    * sin(30°) = ST / (8√2)<BR>\n" );
document.write( "    * ST = 8√2 * sin(30°)<BR>\n" );
document.write( "    * ST = 8√2 * (1/2)<BR>\n" );
document.write( "    * **ST = 4√2**<BR>\n" );
document.write( "    * **ST ≈ 5.66**\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* **simplest radical form RS = 4√6**<BR>\n" );
document.write( "* **approximation RS ≈ 9.80**<BR>\n" );
document.write( "* **simplest radical form ST = 4√2**<BR>\n" );
document.write( "* **approximation ST ≈ 5.66**\r<BR>\n" );
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document.write( "**Note:** \r<BR>\n" );
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document.write( "* Please double-check the given value of ∠STV. If it is indeed 150°, the calculations will need to be adjusted accordingly. <BR>\n" );
document.write( "* This solution assumes that ∠STV = 30° for a valid solution within the context of a right triangle.<BR>\n" );
document.write( " </SPAN>\n" );
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