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.
My work: 10^2 + 16^2 = x^2 x = 2sqrt(89) 
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You correctly found the length of the diagonal, however they are asking for the
smaller angle formed by the diagonals.
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Drawinging this out would help make it understandable
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Find one angle (A) of the right triangle using the tangent
Tan(A) = 10/16
A = 32 degrees
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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;
Subtract those two angles from 180 - 58 - 58 = 64 degrees is the smaller angle
formed by the two diagonals.
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Hope this made sense