Answer
$28.3\ ft$
Work Step by Step
Step 1. Draw a diagram as shown in the figure, where $x$ is the height of the building.
Step 2. Using the Pythagorean's Theorem in the right triangle, we have $x^2+10^2=30^2$ or $x^2=900-100=800$
Step 3. Discard the negative solution; we have $x=\sqrt {800}=20\sqrt 2\approx28.3\ ft$
