document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169496>Question 1169496</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The figure below is a diagram that shows how Colleen estimates the height of a tree that is on the other side of a stream. She stands at point A facing the tree and finds the angle of elevation from A to the top of the tree to be 59°. Then she turns 110° and walks 25 feet to point B, where she measures the angle between her path AB and the line BC extending from her to the base of the tree. She finds that angle to be 36°. Use this information to find the height of the tree. (Round your answer to the nearest whole number.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794611 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=794611\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The figure below is a diagram that shows how Colleen estimates the height of a tree that is on the other side of a stream.<BR>\n" );
document.write( " She stands at point A facing the tree and finds the angle of elevation from A to the top of the tree to be 59°.<BR>\n" );
document.write( " Then she turns 110° and walks 25 feet to point B, where she measures the angle between her path AB and the line BC extending from her to the base of the tree.<BR>\n" );
document.write( " She finds that angle to be 36°. Use this information to find the height of the tree. (Round your answer to the nearest whole number.)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the distance from the observer to the base of the tree. Triangle ABC<BR>\n" );
document.write( "Where A = 110 degrees, B = 36 degrees and c = 25 ft<BR>\n" );
document.write( "Find C: 180 - 110 - 36 = 34 degrees<BR>\n" );
document.write( "Use the law of sines to find b, the distance from A to C (the base of the tree)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fsin%2836%29 ALIGN=MIDDLE  ALT=\"b%2Fsin%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2Fsin%2834%29 ALIGN=MIDDLE  ALT=\"25%2Fsin%2834%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cross multiply<BR>\n" );
document.write( "sin(34)b = sin(36)*25<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14.7%2Fsin%2834%29 ALIGN=MIDDLE  ALT=\"14.7%2Fsin%2834%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 26.278 ft from A to the base of the tree.<BR>\n" );
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document.write( "Find the height of the tree.<BR>\n" );
document.write( "A right triangle is formed, ACT(top of the tree)<BR>\n" );
document.write( "Let h = the height of the tree<BR>\n" );
document.write( "Use the tangent of 59 degrees<BR>\n" );
document.write( "tan(59) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2F26.278 ALIGN=MIDDLE  ALT=\"h%2F26.278\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = tan(59) * 26.278<BR>\n" );
document.write( "h = 43.73 ~ 44 ft is the height of the tree. </SPAN>\n" );
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