Question #1b1d7

1 Answer
tcw1
Aug 1, 2017

#(4sqrt41)/41#

Explanation:

The sketch looks like this:enter image source here
Since we know that the arctan of the angle is #5/4#, we know that the ratio of the opposite side to the adjacent side is 5:4. Note that these are not given values, but a known ratio. Using the Pythagorean Theorem, we know that the hypotenuse is proportional to #sqrt41#. Although we do not know the exact value of the angle, we can find its cosine from its side length ratios. The cosine of this angle is #4/sqrt41#, which simplifies to #(4sqrt41)/41#

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