Given that the mean \(\mu = 1.62\) m and the probability \(P(X > 1.8) = 0.15\), we need to find \(\sigma\).

First, find the z-score corresponding to a probability of 0.15 in the standard normal distribution table. This gives \(z = 1.037\).

Using the standardization formula:

\(z = \frac{X - \mu}{\sigma}\)

Substitute the known values:

\(1.037 = \frac{1.8 - 1.62}{\sigma}\)

Solve for \(\sigma\):

\(\sigma = \frac{0.18}{1.037} = 0.174\)