Answer:
DG=8.62
Step-by-step explanation:
DG is also the hypotenuse. Use the sine ratio. Insert values:
[tex]sineX=\frac{opposite}{hypotenuse}\\\\sin72=\frac{8.2}{x}[/tex]
Solve for x. Multiply both sides by x:
[tex]x*(sin72)=x*(\frac{8.2}{x} )[/tex]
[tex]x*sin72=8.2[/tex]
Divide both sides by sin 72:
[tex]\frac{x*sin72}{sin72}=\frac{8.2}{sin72}[/tex]
[tex]x=\frac{8.2}{sin72}[/tex]
Insert into a calculator:
[tex]x=8.622[/tex]
Round to the nearest hundredth:
[tex]x=8.62[/tex]
Done.
