Question

Solve the variables. See the photo below.

Answer 1

x = 32 y=
`(8)/(√(3) )`

Explanation:

solving for x

take 45 degree as reference angle

using sin rule

sin 45 = opposite / hypotenuse

`(1)/(√(2) ) = (x)/(4√(2) )`

do cross multiplication

`4√(2) * 1 = x * √(2)`

`(4√(2) )/(√(2) ) = x`

root 2 and root 2 gets cancel.Then ,

x = 4

solving for y

take 60 degree as reference angle

using sin rule

sin 60 = opposite / hypotenuse

`(√(3) )/(2) = (x)/(y)`

just now we found the value of x i.e 4 now substitute the value of x here.

`(√(3) )/(2) = (4)/(y)`

do cross multiplication

`2*4 = y * √(3)`

`(8)/(√(3) ) = y`

Answer 2

`x=4; \ y=(8)/(√(3)).`

Explanation:

1) in the triangle with the angles 45; 90 and 45°: x=4√2/√2=4;

2) in the triangle with the angles 60; 90 and 30°: y=x/sin60°= 4/(√3/2)=8/√3