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Answer :

Loneguygo

[tex]\sin 30^{\circ} = \dfrac{LJ}{8\sqrt 2}\\\\\implies LJ = 8\sqrt 2 \sin 30^{\circ} =8\sqrt 2 \cdot \dfrac 12 = 4\sqrt 2\\\\ \text{Now,}\\\sin 45^{\circ} = \dfrac{LM}{LJ} \\\\\implies LM = \sin 45^{\circ} LJ\\\\\implies x = \dfrac 1{\sqrt 2} \cdot 4\sqrt 2 = 4 ~~ units.[/tex]

Fieryanswererftgo

Answer:

x = 4

Explanation:

[tex]\sf sin(x)= \dfrac{opposite}{hypotensue}[/tex]

Solve for LJ:

[tex]\hookrightarrow \sf sin(30) = \dfrac{LJ}{8\sqrt{2} }[/tex]

[tex]\hookrightarrow \sf sin(30)*8\sqrt{2} ={LJ}[/tex]

[tex]\hookrightarrow \sf {LJ} = 4\sqrt{2}[/tex]

Solve for LM:

[tex]\hookrightarrow \sf \sf sin(45)= \dfrac{LM}{4\sqrt{2} }[/tex]

[tex]\hookrightarrow \sf \sf sin(45)*4\sqrt{2} = {LM}[/tex]

[tex]\hookrightarrow \sf {LM} = 4[/tex]

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