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

Answer 1

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.