document.write( "Question 1202974: Hi,
\n" ); document.write( "Can you help me with the question below:
\n" ); document.write( "From a point P due south of a vertical tower, the angle of elevation of the top of the tower is 20 degrees . From a point Q situated 40 metres from P and due east of the tower, the angle of elevation is 35 degrees . Let h metres be the height of the tower.
\n" ); document.write( "a. Draw a diagram to represent the situation.
\n" ); document.write( "b. Evaluate h correct to the nearest metre\r
\n" ); document.write( "\n" ); document.write( "Thank you
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Algebra.Com's Answer #838193 by ikleyn(52835) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Hi,
\n" ); document.write( "Can you help me with the question below:
\n" ); document.write( "From a point P due south of a vertical tower, the angle of elevation
\n" ); document.write( "of the top of the tower is 20 degrees .
\n" ); document.write( "From a point Q situated 40 metres from P and due east of the tower,
\n" ); document.write( "the angle of elevation is 35 degrees . Let h metres be the height of the tower.
\n" ); document.write( "a. Draw a diagram to represent the situation.
\n" ); document.write( "b. Evaluate h correct to the nearest metre
\n" ); document.write( "Thank you
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " I will not make a diagram for you, since I assume that it is your job.\r
\n" ); document.write( "\n" ); document.write( " I will solve the problem, instead.\r
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document.write( "The distance from the base of the tower to point P horizontally in the southern direction is\r\n" );
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document.write( "     = .\r\n" );
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document.write( "The distance from the base of the tower to point Q horizontally in the eastward direction is\r\n" );
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document.write( "     = .\r\n" );
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document.write( "  and    are the legs of a right angled triangle, whose hypotenuse is 40 meters.\r\n" );
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document.write( "So, we write the Pythagorean equation\r\n" );
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document.write( "     +  = .    (1)\r\n" );
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document.write( "Substituting the values of tan(20°) = 0.363970  and  tan(35°) = 0.70021  and making all necessary calculations,\r\n" );
document.write( "I reduce equation (1)  to \r\n" );
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document.write( "    7.548642*h^2 + 2.03959*h^2 = 1600,\r\n" );
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document.write( "or  9.588234*h^2 = 1600,\r\n" );
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document.write( "which gives   h =  = 12.92 meters.\r\n" );
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document.write( "Rounding to the nearest meter, I get the ANSWER  h = 13 meters.\r\n" );
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\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
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