document.write( "Question 1201106: A vertical aerial AB 9.6m high stands on ground which is inclined 12 degrees to the horizontal. A stay connects the top of the aerial A to a point C on the ground 10m downhill from B the foot of the aerial. Determine the length of the stay and the angle the stay makes with the ground. \n" ); document.write( "

Algebra.Com's Answer #853552 by ikleyn(53560) $\"\"$ $\"About$

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\n" ); document.write( "A vertical aerial AB 9.6m high stands on ground which is inclined 12 degrees to the horizontal.
\n" ); document.write( "A stay connects the top of the aerial A to a point C on the ground 10m downhill from B the foot of the aerial.
\n" ); document.write( "Determine the length of the stay and the angle the stay makes with the ground.
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\n" ); document.write( "\n" ); document.write( "        @mananth incorrectly interpreted the given conditions,\r
\n" ); document.write( "\n" ); document.write( "        so his solution is incorrect. The problem says \r
\n" ); document.write( "\n" ); document.write( "        \"A stay connects the top of the aerial A to a point C on the ground 10m $\"highlight%28downhill%29\"$ from B the foot of the aerial\",\r
\n" ); document.write( "\n" ); document.write( "        but @mananth interpreted in his solution as if\r
\n" ); document.write( "\n" ); document.write( "        \"A stay connects the top of the aerial A to a point C on the ground 10m $\"highlight%28uphill%29\"$ from B the foot of the aerial\".\r
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\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
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document.write( "We have triangle ABC with side AB of 9.6 m, side BC of 10 m\r\n" );
document.write( "and angle ABC of 90° + 12° = 102°.\r\n" );
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document.write( "We want to find side AC opposite to angle ABC.\r\n" );
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document.write( "Use the law off cosines\r\n" );
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document.write( "AC^2  = AB^2 + BC^2 −2*AB*BC*cos(∠ABC) = \r\n" );
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document.write( "      = 9.6^2 + 10^2 - 2*10*9.6*cos(102°) = 92.16 + 100 - 2*9.6*10*(-0.20791169081) = 232.0790446.\r\n" );
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document.write( "So, length of the stay AC  is   =  15.234 m.\r\n" );
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document.write( "To find the angle ACB, which the stay makes with the ground, use the Law of sines \r\n" );
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document.write( "    sin(∠ACB)/AB = sin(∠ABC)/AC,\r\n" );
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document.write( "    sin(∠ACB) =  =  = 0.616398646.\r\n" );
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document.write( "Hence,  ∠ACB = arcsin(0.616398646) = 38°  (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved correctly and completely.\r
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