document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=924982>Question 924982</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airplane takes off at a 15° angle and travels at the rate of 350 ft/sec. Approximately how long does it take the airplane to reach an altitude of 25,000 feet? (Round your answer to two decimal places.)<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 #561233 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=561233\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you draw out the triangle, you get \r<BR>\n" );
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document.write( "* <font color=\"blue\">y</font> is the height of the airplane at time t (y is the opposite side)\r<BR>\n" );
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document.write( "* <font color=\"red\">350t</font> represents how far along the hypotenuse the plane has traveled\r<BR>\n" );
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document.write( "* t is time in seconds\r<BR>\n" );
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document.write( "From the drawing above, we see \r<BR>\n" );
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document.write( "<font color=\"blue\">opposite</font> = <font color=\"blue\">y</font>\r<BR>\n" );
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document.write( "<font color=\"red\">hypotenuse</font> = <font color=\"red\">350t</font> \r<BR>\n" );
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document.write( "So that means we can say\r<BR>\n" );
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document.write( "sin(theta) = <font color=\"blue\">opposite</font>/<font color=\"red\">hypotenuse</font>\r<BR>\n" );
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document.write( "sin(15) = <font color=\"blue\">y</font>/<font color=\"red\">350t</font>\r<BR>\n" );
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document.write( "sin(15) = y/350t\r<BR>\n" );
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document.write( "350t*sin(15) = y\r<BR>\n" );
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document.write( "(350*sin(15))*t = y\r<BR>\n" );
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document.write( "y = (350*sin(15))*t\r<BR>\n" );
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document.write( "The function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28350%2Asin%2815%29%29%2At ALIGN=MIDDLE  ALT=\"y+=+%28350%2Asin%2815%29%29%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents how high the plane is at time t.\r<BR>\n" );
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document.write( "y is the vertical distance.<BR>\n" );
document.write( "t is time in seconds.\r<BR>\n" );
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document.write( "Plug in y = 25,000 and solve for t\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28350%2Asin%2815%29%29%2At ALIGN=MIDDLE  ALT=\"y+=+%28350%2Asin%2815%29%29%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25000+=+%28350%2Asin%2815%29%29%2At ALIGN=MIDDLE  ALT=\"25000+=+%28350%2Asin%2815%29%29%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25000%2F%28350%2Asin%2815%29%29+=+t ALIGN=MIDDLE  ALT=\"25000%2F%28350%2Asin%2815%29%29+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+25000%2F%28350%2Asin%2815%29%29 ALIGN=MIDDLE  ALT=\"t+=+25000%2F%28350%2Asin%2815%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+275.978807511162 ALIGN=MIDDLE  ALT=\"t+=+275.978807511162\"   DISABLED_style= \"max-width:90%; height:auto;\" > ... use a <a  rel=nofollow HREF=\"http://web2.0calc.com/\">calculator</a> here (type in \"<font color=\"blue\">25000/(350*sin(15))</font>\" without quotes). \r<BR>\n" );
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document.write( "Special Note: make sure you're in degree mode and NOT in radian mode.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+275.98 ALIGN=MIDDLE  ALT=\"t+=+275.98\"   DISABLED_style= \"max-width:90%; height:auto;\" > ... round to 2 decimal places\r<BR>\n" );
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document.write( "It takes approximately <font size=5 color=\"red\">275.98 seconds</font> for the airplane to climb to 25,000 ft. So that is your answer.\r<BR>\n" );
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document.write( "Note: 275.98 seconds = 4 minutes, 35.98 seconds = 4.6 minutes (approximate). This is extra info to possibly think of the timeframe in an easier context. </SPAN>\n" );
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