



 
Anthony, Are you sure the table has a radius of 100m? That's almost large enough to bee the roof of a football stadium. First, one should subtract 50 from the legs to put the centre C of the table at the origin. The point P, which is at the top of the leg which stands on the positive Xaxis, is a distance PL = 5 am above the XYplane. CP = 100 am and hence, by Pythagoras theorem, CL = 5√399 am Hence P has coordinates (5√399, 0, 5). Similarly the point Q, directly above the Yaxis has coordinates (0, 20√24, 20). The points C, P and Q can then be used to write the equation of the plane which contains the surface of the table. We got the equation to be
The slope of the table top is steepest in the direction of the gradient and the gradient of this function is in the direction √24 i + √399 j. XYPlane Hence the measure of the angle θ is tan^{1}(√399/√24) = 76.2 degrees. Chris and Harley  


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