Answer
The height of the lamppost is\[\text{12}\text{.5 ft}\].
Work Step by Step
When the two figures have same shape but not necessarily the same size, then these figures is known as similar figures.
The given figure satisfies the above mentioned property. Hence, the given triangles are called similar triangles. In similar triangles, the corresponding angles are of same measure and the corresponding sides are proportional.
So that by applying cross-products principle, value of x is:
\[\begin{align}
& \frac{x}{5}=\frac{15}{6} \\
& 6x=75 \\
& x=\frac{75}{6} \\
& x=12.5 \\
\end{align}\]
Hence, the height of the lamppost is\[\text{12}\text{.5 ft}\].
