ANSWER
[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]
EXPLANATION
[tex] \sin(x) = \frac{Opposite}{hypotenuse} [/tex]
[tex]\sin(x) = \frac{3}{4} [/tex]
This means the opposite side is 3 units and the hypotenuse is 4 units.
We use Pythagoras Theorem to find
[tex] { |ZX| }^{2} + {3}^{2} = {4}^{2} [/tex]
[tex]{ |ZX| }^{2} +9=16[/tex]
[tex]{ |ZX| }^{2} =16 - 9[/tex]
[tex]{ |ZX| }^{2} = 7[/tex]
[tex]{ |ZX| } = \sqrt{7} [/tex]
[tex] \tan(x) = \frac{opposite}{adjacent} [/tex]
[tex] \tan(x) = \frac{3}{ \sqrt{7} } [/tex]
[tex] \tan(x) = \frac{3}{ \sqrt{7} } \times \frac{\sqrt{7}}{\sqrt{7}} [/tex]
[tex]\tan(x) = \frac{3\sqrt{7}}{7} [/tex]
