document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199090>Question 1199090</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A flagpole is perpendicular to the horizontal but is on a slope that rises 8.6° from the horizontal. The pole casts a 70-foot shadow down the slope and angle of elevation of the sun measured from the slope is 24.3°. How tall is the pole? Round your answer to the nearest 0.1 foot. </SPAN>\n" );
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document.write( "\"A flagpole is perpendicular to the horizontal\" is another way of saying \"the flagpole is vertical\".\r<BR>\n" );
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document.write( "One way to draw out the diagram:<BR>\n" );
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document.write( "Points:<BR>\n" );
document.write( "A = base of the hill<BR>\n" );
document.write( "B = tip of the shadow<BR>\n" );
document.write( "C = base of the flagpole<BR>\n" );
document.write( "D = top of the flagpole<BR>\n" );
document.write( "E = point used to help label the 8.6 degree angle of elevation\r<BR>\n" );
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document.write( "Given info:<BR>\n" );
document.write( "angle EAB = 8.6 degrees<BR>\n" );
document.write( "angle DBC = 24.3 degrees<BR>\n" );
document.write( "segment BC = 70 ft = shadow length<BR>\n" );
document.write( "The flagpole itself is in red (segment CD).\r<BR>\n" );
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document.write( "Next we draw a horizontal line through point C.<BR>\n" );
document.write( "Mark points F and G on the new horizontal line and line AC respectively.\r<BR>\n" );
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document.write( "Because AE and CF are horizontal parallel lines, we know that <BR>\n" );
document.write( "angle EAB = angle FCG = 8.6 degrees<BR>\n" );
document.write( "and this is because of the corresponding angles theorem.\r<BR>\n" );
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document.write( "Mark point H somewhere to the left of C on the line CF.<BR>\n" );
document.write( "I'll place H as the intersection of CF and BD. <BR>\n" );
document.write( "It doesn't matter where H is as long as it's to the left of C.\r<BR>\n" );
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document.write( "The introduction of point H is to help label the angle HCB which is congruent to angle FCG<BR>\n" );
document.write( "angle HCB = angle FCG = 8.6 degrees<BR>\n" );
document.write( "since these are vertical angles.\r<BR>\n" );
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document.write( "This is the updated diagram with those items added<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=math_tutor2020&illustration_name=Screenshot_187.png\"><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "angle BCD = (angle HCB)+(angle HCD)<BR>\n" );
document.write( "angle BCD = (8.6)+(90)<BR>\n" );
document.write( "angle BCD = 98.6 degrees<BR>\n" );
document.write( "This is angle C of triangle BCD.\r<BR>\n" );
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document.write( "Keeping our focus on triangle BCD only, we can say:<BR>\n" );
document.write( "B+C+D = 180<BR>\n" );
document.write( "24.3+98.6+D = 180<BR>\n" );
document.write( "122.9+D = 180<BR>\n" );
document.write( "D = 180-122.9<BR>\n" );
document.write( "D = 57.1<BR>\n" );
document.write( "This is angle BDC\r<BR>\n" );
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document.write( "We'll still keep our focus on triangle BCD only.<BR>\n" );
document.write( "Apply the law of sines to find side 'b', aka segment CD.\r<BR>\n" );
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document.write( "b/sin(B) = d/sin(D)<BR>\n" );
document.write( "b/sin(24.3) = 70/sin(57.1)<BR>\n" );
document.write( "b = sin(24.3)*70/sin(57.1)<BR>\n" );
document.write( "b = 34.308389211743<BR>\n" );
document.write( "b = 34.3<BR>\n" );
document.write( "Therefore, segment CD is roughly 34.3 feet long.\r<BR>\n" );
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document.write( "Answer: The flagpole is <font color=red>approximately 34.3 feet</font> tall.\r<BR>\n" );
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document.write( "This is roughly comparable to about halfway between a 3 and 4 story building, assuming each floor is 10 ft high.<BR>\n" );
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