Using the provided map and scale, determine the direction of The Bowery Ballroom from Hong Kong Supermarket, identify the restaurant east of Hong Kong Supermarket, and calculate distances between poin

Locate "Hong Kong Supermarket" (point C) and "The Bowery Ballroom" (point B) on the map. Using the compass rose, point B is located to the North-East of point C.

$$\boxed{\text{North-East}}$$

Locate "Hong Kong Supermarket" (point C). Move directly east (to the right) on the map from point C. The restaurant found in that direction is "The Boil".

$$\boxed{\text{The Boil}}$$

Given:
$AC = 452 \text{ m}$
$BC = 483 \text{ m}$
The Theorem of Pythagoras states $AB^2 = AC^2 + BC^2$.

$$AB^2 = (452 \text{ m})^2 + (483 \text{ m})^2$$ $$AB^2 = 204304 \text{ m}^2 + 233289 \text{ m}^2$$ $$AB^2 = 437593 \text{ m}^2$$ $$AB = \sqrt{437593 \text{ m}^2}$$ $$AB \approx 661.51 \text{ m}$$ $$\boxed{661.51 \text{ m}}$$

Given:
Map scale = 1:150 000
Distance on map = 19 mm

First, calculate the real distance in millimeters:

$$\text{Real distance in mm} = \text{Map distance} \times \text{Scale factor}$$ $$\text{Real distance in mm} = 19 \text{ mm} \times 150\,000$$ $$\text{Real distance in mm} = 2\,850\,000 \text{ mm}$$

Next, convert millimeters to meters:
Given $1 \text{ m} = 1000 \text{ mm}$.

$$\text{Real distance in m} = \frac{2\,850\,000 \text{ mm}}{1000 \text{ mm/m}}$$ $$\text{Real distance in m} = 2850 \text{ m}$$

Finally, convert meters to kilometers and round to the nearest km:
Given $1 \text{ km} = 1000 \text{ m}$.

$$\text{Real distance in km} = \frac{2850 \text{ m}}{1000 \text{ m/km}}$$ $$\text{Real distance in km} = 2.85 \text{ km}$$

Rounding to the nearest km:

$$\text{Real distance in km} \approx 3 \text{ km}$$ $$\boxed{3 \text{ km}}$$