Question

Someone plz help me with this asap!!!!!

Answer 1

Answer:

1.) $x=8\sqrt{3};y=16$

2.) $x=1;y=\frac{\sqrt{3}}{2}$

3.) $x=28 ; y=14\sqrt{3}$

4.) $x=24 ; y=12\sqrt{3}$

5.) $x=4\sqrt{3};y=8\sqrt{3}$

6.) $x=\frac{8\sqrt{3}}{3};y=\frac{16\sqrt{3}}{3}$

Step-by-step explanation:

Use the 30°-60°-90° formulas:

a. $longer$ $leg=\sqrt{3}*shorter$ $leg$

b. $hypotenuse=2*shorter$ $leg$

1.) Insert values for a:

$x=\sqrt{3}*8$

Simplify:

$x=8\sqrt{3}$

Insert values for b:

$y=2*8$

Simplify:

$y=16$

2.) Insert values for a:

$y=\sqrt{3}*\frac{1}{2}$

Simplify:

$y=\frac{\sqrt{3}}{2}$

Insert values for b:

$x=2*\frac{1}{2}$

Simplify:

$x=1$

3.) Insert values for a:

$y=\sqrt{3}*14$

Simplify:

$y=14\sqrt{3}$

Insert values for b:

$x=2*14$

Simplify:

$x=28$

4.)Insert values for a:

$y=\sqrt{3}*12$

Simplify:

$y=12\sqrt{3}$

Insert values for b:

$x=2*12$

Simplify:

$x=24$

5.) Insert values for a:

$12=\sqrt{3}*x$

Divide both sides by $\sqrt{3}$ and rationalize:

$\frac{12}{\sqrt{3}}=\frac{\sqrt{3}*x}{\sqrt{3}}\\\\\frac{12}{\sqrt{3}}=x\\\\\frac{\sqrt{3}}{\sqrt{3}}*\frac{12}{\sqrt{3}}\\\\\frac{12\sqrt{3}}{\sqrt{9}}\\\\\frac{12\sqrt{3}}{3}\\\\4\sqrt{3}=x$

Flip:

$x=4\sqrt{3}$

Insert values for b:

$y=2*4\sqrt{3}$

Simplify:

$y=8\sqrt{3}$

6.) Insert values for a:

$8=\sqrt{3}*x$

Divide both sides by $\sqrt{3}$ and rationalize:

$\frac{8}{\sqrt{3}}=\frac{\sqrt{3}*x}{\sqrt{3}}\\\\\frac{8}{\sqrt{3}}=x\\\\\frac{\sqrt{3}}{\sqrt{3}}*\frac{8}{\sqrt{3}}\\\\\frac{8\sqrt{3}}{\sqrt{9}}\\\\\frac{8\sqrt{3}}{3}=x$

Flip:

$x=\frac{8\sqrt{3}}{3}$

Insert values for b:

$y=2*\frac{8\sqrt{3}}{3}$

Simplify:

$y=\frac{16\sqrt{3}}{3}$

Finito.