document.write( "Question 1110603: a pilot flying at 4000 ft approaches a runway and determines that the angles of depression to either end of the runway are 10 degrees and 6 degrees 40' find the length of the runway. \n" ); document.write( "

Algebra.Com's Answer #725603 by KMST(5328) $\"\"$ $\"About$

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A sketch representing the situation is shown below.
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For the a better illustration,
\n" ); document.write( "in the sketch the angles of depression are $\"30%5Eo\"$ and $\"60%5Eo\"$ .
\n" ); document.write( " $\"runway=x-y\"$ ,
\n" ); document.write( " $\"tan%28A%29=h%2Fx\"$ --> $\"x=h%2Ftan%28A%29\"$ ,
\n" ); document.write( " $\"tan%28B%29=h%2Fy\"$ --> $\"y=h%2Ftan%28B%29\"$ .
\n" ); document.write( "With all length in feet,
\n" ); document.write( " $\"h=4000\"$ , $\"A=6%5Eo\"$ $\"%2240+%27%22=%286%262%2F3%29%5Eo=about+6.666667%5Eo\"$ , and $\"B=10%5Eo\"$ ,
\n" ); document.write( "we can calculate a good approximate value of the runway length as
\n" ); document.write( " $\"4000%2Ftan%286.666667%5Eo%29\"$ $\"%22-%22\"$ $\"4000%2Ftan%2810%5Eo%29\"$ $\"%22=%22\"$ $\"4000%2F0.116883\"$ $\"%22-%22\"$ $\"4000%2F0.176327\"$ $\"%22=%22\"$ $\"34222-22685\"$ $\"%22=%22\"$ $\"%22about+11%2C500%22\"$ .
\n" ); document.write( "The length of the runway is about $\"highlight%28%2211%2C500+feet%22%29\"$ .
\n" ); document.write( "We could carry more digits through the calculations,
\n" ); document.write( "and we could calculate the length of the runway as $\"11537feet\"$ ,
\n" ); document.write( "but considering the uncertainty of the altitude and angle measurements
\n" ); document.write( "a more precise result is not more meaningful. \n" ); document.write( "

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