Find x
a. 11√3
b. 33
c. 44√2
d. 33√2

  B.  33

Step-by-step explanation:

The side opposite the 45° angle has measure 11√6×sin(45°). The side opposite the 60° angle has measure tan(60°) times that, so we have ...

  x = 11√6×sin(45°)×tan(60°) = 11√6×(√2/2)×√3 = 11×(√6)²/2

  x = 33

The mnemonic SOH CAH TOA can be a useful reminder of the definitions of the trig functions. It tells you ...

  Sin = Opposite/Hypotenuse

  Tan = Opposite/Adjacent

Using these relations, we can find the sides of interest:

  Opposite = Hypotenuse × Sin . . . . for the 45° triangle

  Opposite = Adjacent × Tan . . . . . . for the 60° triangle

where the side opposite the 45° angle is the side adjacent to the 60° angle.

The Quick answer is B.

Step-by-step explanation: