Answer:
[tex]x=8\\y=6.9[/tex]
Step-by-step explanation:
First find x:
Use the sine ratio since you have the side opposite the given angle and need to know the hypotenuse:
[tex]sine=\frac{opposite}{hypotenuse}[/tex]
Insert values:
[tex]sin30=\frac{4}{x}[/tex]
Isolate x. Multiply both sides be x:
[tex]x*(sin30)=x*(\frac{4}{x})\\\\x*sin30=4[/tex]
Divide both sides by sin30°:
[tex]\frac{x*sin30}{sin30}=\frac{4}{sin30}\\\\x=\frac{4}{sin30}[/tex]
Insert into a calculator:
[tex]x=8[/tex]
Now find y. Use either the cosine or tangent ratio:
[tex]cosine=\frac{adjacent}{hypotenuse}\\\\tangent=\frac{opposite}{adjacent}[/tex]
Insert values:
[tex]cos30=\frac{y}{8}[/tex]
Isolate y. Multiply 8 on both sides:
[tex]8*(cos30)=8*(\frac{y}{8} )\\\\8*cos30=y\\\\y=8*cos30[/tex]
Insert into a calculator:
[tex]y=6.9[/tex]
Finito.
