Answer
$60\sqrt 5\approx 134.2$ meters
Work Step by Step
Let's note by $h$ the height o the building. We draw a right triangle with legs $h$ and $2h$ and hypotenuse of length $300$.
We determine $h$ using the Pythagorean theorem:
$$\begin{align*}
h^2+(2h)^2&=300^2\\
h^2+4h^2&=90,000\\
5h^2&=90,000\\
h^2&=\dfrac{90,000}{5}\\
h^2&=18,000\\
h&=\pm\sqrt{18,000}=\pm 60\sqrt 5\approx \pm 134.2.
\end{align*}$$
Because $h>0$, the only solution is $60\sqrt 5\approx 134.2$ meters.
