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How do I find the Tangent if Sine is equal to (4/9)?

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2 Answers

Sin A =  opposite side/ Hypotenuse = 4/9 
 
            You know in right triangle one leg = 4, hypotenuse 
                                      _____      ___

             Hypotenuse =  sqrt( 92-42) = Sqrt (65 )  = 8.06

Since sin x = opp/hyp, we have
opp = 4
hyp = 9
adj = sqrt(9^2-4^2) = sqrt(65)
tan x = +/- adj/hyp = +/- sqrt(65)/4, where "+" for the tan x in the first quadrant, and "-" in the second quadrant.

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