Answer
$134\ m$
Work Step by Step
Step 1. Draw a diagram as shown in the figure. The height of the building is $x$ meters.
Step 2. Using the Pythagorean Theorem, we have $x^2+(2x)^2=300^2$ or $5x^2=300^2$, which gives $x=\frac{300}{\sqrt 5}\approx134\ m$
