Question

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

Answer 1

1.)
`x=8√(3);y=16`

2.)
`x=1;y=(√(3))/(2)`

3.)
`x=28 ; y=14√(3)`

4.)
`x=24 ; y=12√(3)`

5.)
`x=4√(3);y=8√(3)`

6.)
`x=(8√(3))/(3);y=(16√(3))/(3)`

Explanation:

Use the 30°-60°-90° formulas:

a.
`longer`
`leg=√(3)*shorter`
`leg`

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

1.) Insert values for a:

`x=√(3)*8`

Simplify:

`x=8√(3)`

Insert values for b:

`y=2*8`

Simplify:

`y=16`

2.) Insert values for a:

`y=√(3)*(1)/(2)`

Simplify:

`y=(√(3))/(2)`

Insert values for b:

`x=2*(1)/(2)`

Simplify:

`x=1`

3.) Insert values for a:

`y=√(3)*14`

Simplify:

`y=14√(3)`

Insert values for b:

`x=2*14`

Simplify:

`x=28`

4.)Insert values for a:

`y=√(3)*12`

Simplify:

`y=12√(3)`

Insert values for b:

`x=2*12`

Simplify:

`x=24`

5.) Insert values for a:

`12=√(3)*x`

Divide both sides by
`√(3)` and rationalize:

`(12)/(√(3))=(√(3)*x)/(√(3))\\\\(12)/(√(3))=x\\\\(√(3))/(√(3))*(12)/(√(3))\\\\(12√(3))/(√(9))\\\\(12√(3))/(3)\\\\4√(3)=x`

Flip:

`x=4√(3)`

Insert values for b:

`y=2*4√(3)`

Simplify:

`y=8√(3)`

6.) Insert values for a:

`8=√(3)*x`

Divide both sides by
`√(3)` and rationalize:

`(8)/(√(3))=(√(3)*x)/(√(3))\\\\(8)/(√(3))=x\\\\(√(3))/(√(3))*(8)/(√(3))\\\\(8√(3))/(√(9))\\\\(8√(3))/(3)=x`

Flip:

`x=(8√(3))/(3)`

Insert values for b:

`y=2*(8√(3))/(3)`

Simplify:

`y=(16√(3))/(3)`

Finito.