Question

A student measured the height of a pole as 5.98m, the percentage error made in measuring the height is 5 persent. If this movement is smaller than the exact measurements, find the actual height of the place

Answer 1

To find the actual height of the pole when a measurement is made with a certain percentage error, we can use the concept of percentage error to relate the measured value and the actual value.

The formula for percentage error is given by:

\[
\text{Percentage Error} = \left( \frac{\text{Measured Value} - \text{Actual Value}}{\text{Actual Value}} \right) \times 100
\]

In this case, we know the following:
- Measured Value = 5.98 m
- Percentage Error = 5%

Since the measured value is smaller than the actual value, we can rearrange the formula to find the actual value:

Let \( x \) be the actual height of the pole. According to the given percentage error:

\[
5 = \left( \frac{5.98 - x}{x} \right) \times 100
\]

Now, convert the percentage to a decimal by dividing by 100:

\[
0.05 = \frac{5.98 - x}{x}
\]

To eliminate the fraction, multiply both sides by \( x \):

\[
0.05x = 5.98 - x
\]

Next, add \( x \) to both sides:

\[
0.05x + x = 5.98
\]

This simplifies to:

\[
1.05x = 5.98
\]

Now, solve for \( x \) by dividing both sides by 1.05:

\[
x = \frac{5.98}{1.05} \approx 5.69857
\]

Thus, the actual height of the pole is approximately:

\[
x \approx 5.70 \text{ m}
\] (rounded to two decimal places).

So, the actual height of the pole is approximately **5.70 meters**.