By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by 21

The transmission range of a TV tower is directly proportional to the square root of the height of the tower. This relationship is given by the formula:

R = k * sqrt(h)

where:

• R is the transmission range,
• h is the height of the tower, and
• k is a constant that depends on other factors such as the frequency of the signal.

If the height of the tower is increased by 21%, the new height h' is given by:

h' = h * 1.21

The new transmission range R' is then:

R' = k * sqrt(h')

Substituting h' into the equation gives:

R' = k * sqrt(h * 1.21)

This can be rewritten as:

R' = R * sqrt(1.21)

So the percentage increase in the transmission range is:

% increase = (R' - R) / R * 100%

Substituting R' gives:

% increase = (R * sqrt(1.21) - R) / R * 100%

Simplifying this gives:

% increase = (sqrt(1.21) - 1) * 100%

Calculating this gives approximately:

% increase = 10.05%

So the transmission range of the TV tower will increase by approximately 10.05% when the height of the tower is increased by 21%.