Given that mu = : 1 < x < 20, where x is an integer P = : x is a multiple of 3 \ and Q = : x is a prime number \ where P and Q are subsets of mu, find: (a) P Q'; (b) P' Q; (c) (P Q)'

We have a right-angled triangle TRO.
The distance from the observer to the tower base, $|OR|$, is 84 m.
The angle of elevation from O to T is $57^\circ$.
Let the height of the tower TR be $h$.

In $\triangle TRO$, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.

The observer moves away, and the new angle of elevation is $49^\circ$.
Let the new distance from the tower base to the observer be $OR'$.
Using the height $h$ calculated in part (a) (using the unrounded value for accuracy):

The distance moved backwards is the difference between the new distance and the original distance.
Distance moved $= OR' - OR$
Distance moved $\approx 112.4400 - 84$
Distance moved $\approx 28.4400 \text{ m}$

Distance moved $\approx \boxed{\text{28.44 m}}$