If cos x = a/3 and 0< x< pi/2, then tan x is?

Question

how do you do it?

Answer 1

cos x = adjascent/hypotenuse = a/3

tan x = opposite/adjascent

opposite^2 + adj^2 = hyp^2
opposite = {9 - a^2}^(1/2)

So tan x = {(9 - a^2)^1/2 }/ a

Answer 2

Adjacent = a
Opposite = y
Hypotenuse = 3
3² = a² + y²
y² = 9 - a²
y = √(9 - a²)
tan x = √(9 - a²) / a

Answer 3

tan x = sqrt(9-a^2)/a
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Reason: a-sqrt(9-a^2)-3 forms a right triangle with 3 as the hyp.