Answer: [tex]x=4[/tex]
Step-by-step explanation:
Calculate the lenght of LJ as following:
[tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]
Where:
[tex]\alpha=30\°\\opposite:LJ\\hypotenuse=8\sqrt{2}[/tex]
Substitute values and solve for LJ. Then:
[tex]sin(30\°)=\frac{LJ}{8\sqrt{2}}\\LJ=8\sqrt{2}}*sin(30\°)\\LJ=4\sqrt{2}[/tex]
Calculate the lenght of x as following:
[tex]sin\beta=\frac{opposite}{hypotenuse}[/tex]
Where:
[tex]\beta=45\°\\opposite:x\\hypotenuse=4\sqrt{2}[/tex]
Substitute values and solve for x. Then:
[tex]sin(45\°)=\frac{x}{4\sqrt{2}}\\x=4\sqrt{2}}*sin(45\°)\\x=4\sqrt{2}[/tex]
[tex]x=4[/tex]
