document.write( "Question 438302: A plane flying at a height of 3.5 miles is at point C. At that point the angle of depression to city A is measured to be 48 degrees and the agnle of depression to city B is measured to be 36 degrees. Calculate the distance in miles between cities A and B. \n" ); document.write( "

Algebra.Com's Answer #303160 by htmentor(1343) $\"\"$ $\"About$

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The angle of depression is the angle below the horizontal from the plane to
\n" ); document.write( "each of the cities. This angle is also equal to the angle from the horizontal
\n" ); document.write( "up to the plane from the cities. The tangent of this angle will be equal to
\n" ); document.write( "the height of the plane divided by the distance from the city to the point C along the ground
\n" ); document.write( "Let a = the distance from city A to point C
\n" ); document.write( "Let b = the distance from city B to point C
\n" ); document.write( "For city A we have
\n" ); document.write( "tan(48) = 3.5/a
\n" ); document.write( "And for city B we have
\n" ); document.write( "tan(36) = 3.5/b
\n" ); document.write( "Solve for a and b:
\n" ); document.write( "a = 3.5/tan(48) = 3.151 miles
\n" ); document.write( "b = 3.5/tan(36) = 4.817 miles
\n" ); document.write( "Therefore the distance from city A to city B is:
\n" ); document.write( "3.151 + 4.817 = 7.968 miles \n" ); document.write( "

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