Answer:
1.) [tex]x=8\sqrt{3};y=16[/tex]
2.) [tex]x=1;y=\frac{\sqrt{3}}{2}[/tex]
3.) [tex]x=28 ; y=14\sqrt{3}[/tex]
4.) [tex]x=24 ; y=12\sqrt{3}[/tex]
5.) [tex]x=4\sqrt{3};y=8\sqrt{3}[/tex]
6.) [tex]x=\frac{8\sqrt{3}}{3};y=\frac{16\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Use the 30°-60°-90° formulas:
a. [tex]longer[/tex] [tex]leg=\sqrt{3}*shorter[/tex] [tex]leg[/tex]
b. [tex]hypotenuse=2*shorter[/tex] [tex]leg[/tex]
1.) Insert values for a:
[tex]x=\sqrt{3}*8[/tex]
Simplify:
[tex]x=8\sqrt{3}[/tex]
Insert values for b:
[tex]y=2*8[/tex]
Simplify:
[tex]y=16[/tex]
2.) Insert values for a:
[tex]y=\sqrt{3}*\frac{1}{2}[/tex]
Simplify:
[tex]y=\frac{\sqrt{3}}{2}[/tex]
Insert values for b:
[tex]x=2*\frac{1}{2}[/tex]
Simplify:
[tex]x=1[/tex]
3.) Insert values for a:
[tex]y=\sqrt{3}*14[/tex]
Simplify:
[tex]y=14\sqrt{3}[/tex]
Insert values for b:
[tex]x=2*14[/tex]
Simplify:
[tex]x=28[/tex]
4.)Insert values for a:
[tex]y=\sqrt{3}*12[/tex]
Simplify:
[tex]y=12\sqrt{3}[/tex]
Insert values for b:
[tex]x=2*12[/tex]
Simplify:
[tex]x=24[/tex]
5.) Insert values for a:
[tex]12=\sqrt{3}*x[/tex]
Divide both sides by [tex]\sqrt{3}[/tex] and rationalize:
[tex]\frac{12}{\sqrt{3}}=\frac{\sqrt{3}*x}{\sqrt{3}}\\\\\frac{12}{\sqrt{3}}=x\\\\\frac{\sqrt{3}}{\sqrt{3}}*\frac{12}{\sqrt{3}}\\\\\frac{12\sqrt{3}}{\sqrt{9}}\\\\\frac{12\sqrt{3}}{3}\\\\4\sqrt{3}=x[/tex]
Flip:
[tex]x=4\sqrt{3}[/tex]
Insert values for b:
[tex]y=2*4\sqrt{3}[/tex]
Simplify:
[tex]y=8\sqrt{3}[/tex]
6.) Insert values for a:
[tex]8=\sqrt{3}*x[/tex]
Divide both sides by [tex]\sqrt{3}[/tex] and rationalize:
[tex]\frac{8}{\sqrt{3}}=\frac{\sqrt{3}*x}{\sqrt{3}}\\\\\frac{8}{\sqrt{3}}=x\\\\\frac{\sqrt{3}}{\sqrt{3}}*\frac{8}{\sqrt{3}}\\\\\frac{8\sqrt{3}}{\sqrt{9}}\\\\\frac{8\sqrt{3}}{3}=x[/tex]
Flip:
[tex]x=\frac{8\sqrt{3}}{3}[/tex]
Insert values for b:
[tex]y=2*\frac{8\sqrt{3}}{3}[/tex]
Simplify:
[tex]y=\frac{16\sqrt{3}}{3}[/tex]
Finito.
