document.write( "Question 141710: A circle centered at the origin has a radius of 10.If the point(10,0)is rotated 120 degrees counter-clockwise, determine the coordinates of the new point in exact radical form. \n" ); document.write( "

Algebra.Com's Answer #103269 by Edwin McCravy(20060) $\"\"$ $\"About$

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A circle centered at the origin has a radius of 10.If the point(10,0)is rotated 120 degrees counter-clockwise, determine the coordinates of the new point in exact radical form.
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document.write( "Now we subtract 180°-120° and find that the angle between the slanted\r\n" );
document.write( "line and the left side of the x-axis is 60° (indicated by the green\r\n" );
document.write( "curved line, so we label it 60°:\r\n" );
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document.write( "Now from the point in question we draw a perpendicular down to the\r\n" );
document.write( "x-axis:\r\n" );
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document.write( "This forms a special right triangle.  \r\n" );
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document.write( "We are supposed to know that if a right triangle has an acute angle \r\n" );
document.write( "of 60°, then one of the sides of the 60° angle is one-half the other.\r\n" );
document.write( "So since the hypotenuse is 10, its bottom leg is 5.\r\n" );
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document.write( "That tells us that the x-coordinate of the point in question is .\r\n" );
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document.write( "We can calculate the vertical side of that right triangle by\r\n" );
document.write( "the Pythagorean theorem:\r\n" );
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document.write( "So the coordinates of the point is (,).\r\n" );
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document.write( "Edwin

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