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The right triangle above has side lengths a and b such that 0 < b < a. One of its angles measures arctan(a/b). What is cos(arctan(a/b))?

 

 Aug 20, 2020
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If the angle is   arctan a/b    then it is the angle in the upper left corner because tan = opp/adj

   the cos of that angle is   adj/ hyp =   b / (sqrt(a2+b2)         (because hypot in rt triangle = sqrt(a^2 + b^2)      AND COS = adj / hyp )

 Aug 20, 2020

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