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lyubas
If tan (arc cos radical3/k)=radical3/3 then k is?
We know the tangent of some angle is sqrt3/3. What is that angle?
Ok How about this? Look at arccos(radical 3/k) Label this part y or whatever. So we have \[y=\arccos(\frac{\sqrt{3}}{k})\] which means \[\cos(y)=\frac{\sqrt{3}}{k} \] Label a right triangle with the adjacent side of y being length sqrt(3) and label the hyp with the length k. Then find the opposite side of the angle y using the Pythagorean Theorem.
Then find tan(y) (which we also know as \[\tan(\arccos(\frac{\sqrt{3}}{k}))\])
then compare that value with the other side of the equation.
you will have an algebraic equation.