Question
A student measured the height of a pole as 5.98m. The percentage error made in measuring the height is 15. If this movement is smaller than the exact measurements. Find the actual height of the place
Answers
GPT-4o mini
To find the actual height of the pole when the measured height and percentage error are given, you can use the formula for percentage error:
\[
\text{Percentage Error} = \left( \frac{\text{Error}}{\text{Actual Value}} \right) \times 100
\]
In this case, the measured height is \( 5.98 \, \text{m} \) and the percentage error is \( 15\% \). Since this error is smaller than the actual height, we have:
Let the actual height be \( x \).
First, calculate the error caused by the percentage error:
\[
\text{Error} = \frac{15}{100} \times x = 0.15x
\]
Since the measured height is less than the actual height by this error, we can write:
\[
5.98 = x - 0.15x
\]
This simplifies to:
\[
5.98 = 0.85x
\]
Now, solve for \( x \):
\[
x = \frac{5.98}{0.85}
\]
Calculating that gives:
\[
x \approx 7.04 \, \text{m}
\]
Therefore, the actual height of the pole is approximately **7.04 meters**.
\[
\text{Percentage Error} = \left( \frac{\text{Error}}{\text{Actual Value}} \right) \times 100
\]
In this case, the measured height is \( 5.98 \, \text{m} \) and the percentage error is \( 15\% \). Since this error is smaller than the actual height, we have:
Let the actual height be \( x \).
First, calculate the error caused by the percentage error:
\[
\text{Error} = \frac{15}{100} \times x = 0.15x
\]
Since the measured height is less than the actual height by this error, we can write:
\[
5.98 = x - 0.15x
\]
This simplifies to:
\[
5.98 = 0.85x
\]
Now, solve for \( x \):
\[
x = \frac{5.98}{0.85}
\]
Calculating that gives:
\[
x \approx 7.04 \, \text{m}
\]
Therefore, the actual height of the pole is approximately **7.04 meters**.