Answer: OPTION A.
Step-by-step explanation:
Observe the figure attached.
The first step is the find "a". In order to find this side, we need to use this Trigonometric Identity:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
In this case:
[tex]\alpha=45\°\\\\opposite=12\\\\hypotenuse=a[/tex]
Then, substituting values and solving for "a", we get:
[tex]sin(45 \°)=\frac{12}{a}\\\\a=\frac{12}{sin(45 \°)}\\\\a=12\sqrt{2}[/tex]
Now we must apply this Trigonometric Identity:
[tex]tan\theta=\frac{opposite}{adjacent}[/tex]
In this case:
[tex]\theta=60\°\\\\opposite=12\sqrt{2}\\\\adjacent=x[/tex]
Then, substituting values and solving for "x", we get:
[tex]tan(60\°)=\frac{12\sqrt{2}}{x}\\\\x=\frac{12\sqrt{2}}{tan(60 \°)}\\\\x=4\sqrt{6}[/tex]
