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)

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) (Show Source): You can put this solution on YOUR website!

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. Edwin

Answer by Alan3354(69443) (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

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