document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171560>Question 1171560</A>: <I><SPAN STYLE=\"word-break: break-all;\"> To determine the distance across a lake, a surveyor selected two points P and Q, one on each shore and directly<BR>\n" );
document.write( "opposite each other. On the shore containing P, another point R was chosen, 50 ft from P, so that the line segment PR<BR>\n" );
document.write( "was perpendicular to the line segment PQ. The angle having the sides PR and PQ was measured to be 78.24°. What<BR>\n" );
document.write( "is the distance across the lake? Round off your answer to two decimal places.<BR>\n" );
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document.write( "Diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"50%\" src = \"https://i.imgur.com/WPmms5J.png\"><BR>\n" );
document.write( "The surveyor is on the side labeled \"shore 1\". Point Q could be any landmark on the opposite shore such as a rock or tree.\r<BR>\n" );
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document.write( "I think your teacher made a typo and should have said \"The angle having the sides PR and QR was measured to be 78.24°\". The angle having sides PR and PQ is the 90 degree angle. \r<BR>\n" );
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document.write( "Based on the diagram above, we know that,<BR>\n" );
document.write( "tan(angle) = opposite/adjacent<BR>\n" );
document.write( "tan(angle R) = PQ/PR<BR>\n" );
document.write( "tan(78.24) = x/50<BR>\n" );
document.write( "50*tan(78.24) = x<BR>\n" );
document.write( "x = 50*tan(78.24)<BR>\n" );
document.write( "x = 240.174013162624<BR>\n" );
document.write( "x = 240.17<BR>\n" );
document.write( "Make sure your calculator is in degree mode.\r<BR>\n" );
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document.write( "Answer:  The distance across the lake is approximately 240.17 feet<BR>\n" );
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