ANSWER
[tex]{ \tan(y) } = \frac{ \sqrt{7} }{3}[/tex]
EXPLANATION
If
[tex] \sin(X )= \frac{3}{4} [/tex]
[tex] \sin(X )= \frac{opposite}{hypotenuse} [/tex]
This implies that the opposite is 3 units and the hypotenuse is 4 units.
We now find the adjacent side using the Pythagoras Theorem.
[tex] {a}^{2} + {o}^{2} = {h}^{2} [/tex]
[tex] {a}^{2} + {3}^{2} = {4}^{2} [/tex]
[tex]{a}^{2} + 9 =16[/tex]
[tex] {a}^{2} =16 - 9[/tex]
[tex]{a}^{2} = 7[/tex]
[tex]{a}= \sqrt{7} [/tex]
[tex] { \tan(y) } = \frac{opposite}{adjacent} [/tex]
The side opposite to Y is √7 and the side adjacent to Y is 3.
[tex] { \tan(y) } = \frac{ \sqrt{7} }{3} [/tex]
