.

To solve this problem, we can use similar triangles.

From the diagram:

• The height of the pole with the lamp is \( h = 8 \) meters.
• The person is standing at a distance \( a = 14 \) meters from the pole.
• The length of the shadow is \( b = 3.5 \) meters.

Let's denote the height of the person as \( x \).

Using the properties of similar triangles, the ratios of corresponding sides are equal:

\[ \frac{x}{b} = \frac{h}{a + b} \]

Substituting the known values:

\[ \frac{x}{3.5} = \frac{8}{14 + 3.5} \]

Simplify \( 14 + 3.5 = 17.5 \), so the equation becomes:

\[ \frac{x}{3.5} = \frac{8}{17.5} \]

Cross-multiply to solve for \( x \):

\[ x \times 17.5 = 3.5 \times 8 \]

\[ x \times 17.5 = 28 \]

\[ x = \frac{28}{17.5} \]

\[ x = 1.6 \]

So the height of the person is 1.6 meters.