SOLUTION: Given that X is an acute angle and COS X = (2√5)/5, find tan (90-x)Given that X is an acute angle and COS X = (2√5)/5, find tan (90-x)

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Question 1189035: Given that X is an acute angle and COS X = (2√5)/5, find tan (90-x)Given that X is an acute angle and COS X = (2√5)/5, find tan (90-x)
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!

cos%28x%29+=+%282sqrt%285%29%29%2F5+=+adjacent%2Fhypotenuse

Draw a right triangle with angle x, adjacent side=2√5 and hypotenuse=5, then
use Pythagorean theorem to get the opposite side. Then simplify the opposite
side.









tan%2890%5Eo-x%29%22%22=%22%22opposite%2Fadjacent%22%22=%22%22%282sqrt%285%29%29%2Fsqrt%285%29%22%22=%22%222

Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Given that x is an acute angle and cos(x) = (2√5)/5, find tan (90-x)
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cos(x) = sin(90-x) = 2sqrt(5)/5
Call (90-x) y
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sin(y) = 2sqrt(5)/5
cos(y) = sqrt(1 - sin^2(y)) = sqrt(1 - 20/25) = sqrt(1/5) =sqrt(5)/5
tan(y) = sin(y)/cos(y) = 2sqrt(5)/5)/(sqrt(5)/5) = 2