Question

Can someone help me with this!!!!!

Answer 1

30.
`x=5\\y=5√(3)`

31.
`x=4\\y=4√(3)`

32.
`x=6\\y=6√(3)`

33.
`x=4.5\\y=(9√(3) )/(2)`

34.
`x=40\\y=40√(3)`

35.
`x=7.5\\y=(15√(3) )/(2)`

Explanation:

Use SOHCAHTOA to find one of the missing sides, then use the pythagorean theorem (
`x^(2)+ y^(2) =z^(2)`) to find the other one

`sin=(opposite)/(hypotenuse)`

`cos=(adjacent)/(hypotenuse)`

`tan=(opposite)/(adjacent)`

30.

First find
`x` using Sin

`sin(30)=(x)/(10)`

`10*sin(30)=x`

`x=5`

Then use the pythagorean theorem to find
`y`

`5^(2)+ y^(2) =10^(2)`

`25+y^(2) =100`

`y^(2) =75`

`\sqrt{y^(2)} =√(75)`

`y=5√(3)`

32.

First use Sin to find
`x`

`sin(30)=(x)/(8)`

`8*sin(30)=x`

`x=4`

Then use the pythagorean theorem to find
`y`

`4^(2)+ y^(2) =8^(2)`

`16+y^(2) =64`

`y^(2) =48`

`\sqrt{y^(2) } =√(48)`

`y=4√(3)`

32.

First use Sin to find
`x`

`sin(30)=(x)/(12)`

`12*sin(30)=x`

`x=6`

Then use the pythagorean theorem to find
`y`

`6^(2)+ y^(2) =12^(2)`

`36+y^(2) =144`

`y^(2) =108`

`\sqrt{y^(2) } =√(108)`

`y=6√(3)`

33.

First use Sin to find
`x`

`sin(30)=(x)/(9)`

`9*sin(30)=x`

`x=4.5`

Then use the pythagorean theorem to find
`y`

`4.5^(2)+ y^(2) =9^(2)`

`20.25+y^(2) =81`

`y^(2) =60.75`

`\sqrt{y^(2) } =√(60.75)`

`y=(9√(3) )/(2)`

34.

First use Sin to find
`x`

`sin(30)=(x)/(80)`

`80*sin(30)=x`

`x=40`

Then use the pythagorean theorem to find
`y`

`40^(2)+ y^(2) =80^(2)`

`1600+y^(2) =6400`

`y^(2) =4800`

`\sqrt{y^(2) } =√(4800)`

`y=40√(3)`

35.

First use Sin to find
`x`

`sin(30)=(x)/(15)`

`15*sin(30)=x`

`x=7.5`

Then use the pythagorean theorem to find
`y`

`7.5^(2)+ y^(2) =15^(2)`

`56.25+y^(2) =225`

`y^(2) =168.75`

`\sqrt{y^(2) }=√(168.75)`

`y=(15√(3) )/(2)`