Please help for number 8 I don't understand.

8a. x = 16√3

8b. y = 8√3

Step-by-step explanation:

8a. Determination of the value of x

Adjacent = 24

Hypothenus = x

Angle θ = 30°

The value of x can be obtained by using cosine ratio as illustrated below:

Cos θ = Adjacent /Hypothenus

Cos 30 = 24 / x

√3/2 = 24/x

Cross multiply

x × √3 = 2× 24

x × √3 = 48

Divide both side by √3

x = 48/√3

Rationalise

x = 48/√3 × √3/√3

x = 48√3 / √3 × √3

x = 48√3 / 3

x = 16√3

8b. Determination of the value of y

Opposite = y

Adjacent = 24

Angle θ = 30°

The value of y can be obtained by using Tan ratio as illustrated below:

Tan θ = Opposite / Adjacent

Tan 30 = y / 24

1 / √3 = y /24

Cross multiply

y × √3 = 1 × 24

y × √3 = 24

Divide both side by √3

y = 24 /√3

Rationalise

y = 24 /√3 × √3/√3

y = 24 ×√3 / √3 × √3

y = 24√3 / 3

y = 8√3