document.write( "Question 79650: The sides of a rectangle are 10 and 16. Find, to the nearest degree, one of the smaller angles formed at the intersection of the diagonals.\r
\n" ); document.write( "\n" ); document.write( "My work: $\"10%5E2+%2B+16%5E2+=+x%5E2\"$ $\"x+=+2sqrt%2889%29\"$ \n" ); document.write( "

Algebra.Com's Answer #57232 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The sides of a rectangle are 10 and 16. Find, to the nearest degree, one of the smaller angles formed at the intersection of the diagonals.
\n" ); document.write( "My work: 10^2 + 16^2 = x^2 x = 2sqrt(89)
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\n" ); document.write( "You correctly found the length of the diagonal, however they are asking for the
\n" ); document.write( "smaller angle formed by the diagonals.
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\n" ); document.write( "Drawinging this out would help make it understandable
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\n" ); document.write( "Find one angle (A) of the right triangle using the tangent
\n" ); document.write( "Tan(A) = 10/16
\n" ); document.write( "A = 32 degrees
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\n" ); document.write( "That would make the two equal angles in the isosceles triangle, formed by the short side (10) and two halves of the diagonals: 90 - 32 = 58 degrees;
\n" ); document.write( "Subtract those two angles from 180 - 58 - 58 = 64 degrees is the smaller angle
\n" ); document.write( "formed by the two diagonals.
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\n" ); document.write( "Hope this made sense \n" ); document.write( "

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