Answer:
Option D. 11√6/2
Step-by-step explanation:
We'll begin by calculating the side opposite to angle 60°.
This is illustrated below:
Angle θ = 60°
Opposite =?
Hypothenus = 11
Using the sine ratio, we can obtain the side opposite to angle 60° as follow:
Sine θ = Opposite/Hypothenus
Sine 60 = Opposite /11
Cross multiply
Opposite = 11 × Sine 60
Sine 60 = √3/2
Opposite = 11 × √3/2
Opposite = 11√3/2
Finally, we shall determine the value of x as follow:
Angle θ = 45°
Opposite = 11√3/2
Hypothenus = x
Using the sine ratio, we can obtain the value of x as shown below:
Sine θ = Opposite/Hypothenus
Sine 45° = 11√3/2 /x
Cross multiply
x × Sine 45° = 11√3/2
Sine 45° = 1/√2
x × 1/√2 = 11√3/2
x/√2 = 11√3/2
Multiply through by √2
x = √2 × 11√3/2
x = 11√6/2
