Calculate the height of a radio, television and telecommunications tower where the scale is 1:11 000; r = 70 mm; d = 7 mm and H = 950 m. Round the answer to first decimal. The height of the tower is:

The problem asks to calculate the height of a tower. We are given:

• Scale: $1:11 000$
• $r = 70$ mm
• $d = 7$ mm
• $H = 950$ m

The instruction "Calculate the height" implies that we need to perform a computation using the given scale. If $H=950$ m were the height of the tower, no calculation would be necessary. Therefore, we assume that one of the measurements in millimeters ($r$ or $d$) represents the height of the tower on a map or drawing. We will use $r=70$ mm as the map height for the calculation, as it is a more substantial measurement for a tall telecommunications tower.

The scale $1:11 000$ means that 1 unit on the map corresponds to $11 000$ units in reality.
Map height $= 70$ mm
Real height $= \text{Map height} \times \text{Scale factor}$

$$\text{Real height} = 70 \text{ mm} \times 11 000$$ $$\text{Real height} = 770 000 \text{ mm}$$

Since 1 meter (1 m) is equal to 1000 millimeters (1000 mm), we divide the real height in millimeters by 1000 to get the height in meters.

$$\text{Real height} = \frac{770 000 \text{ mm}}{1000 \text{ mm/m}}$$ $$\text{Real height} = 770 \text{ m}$$

The calculated real height is 770 m. Rounding this to the first decimal place, as per the example given in the question (e.g., 123 becomes 123,0), gives:

$$770.0 \text{ m}$$