A balloon moving in a straight line passes vertically above two...

In& $∆ ABE$,
$tan {30}^{o} = \dfrac{h}{300} ⇒ h = 100\sqrt{3}ft$ … \left(1\right)$<br />and in$\Delta ABD$,<br />$tan {45}^{o} = \dfrac{H}{300} ⇒ H = 300ft&hellip; \left(2\right)
Also, $\dfrac{H}{AC} = \dfrac{h}{BC}$ (Similar triangles)
$⇒ \dfrac{300}{300 + x} = \dfrac{100\sqrt{3}}{x}$ [using Eq. \left(1\right)$and \left(2\right)$ ]
$⇒ \sqrt{3}x = 300 + x$
$⇒ x = \dfrac{300}{\sqrt{3} - 1} = 150\left(\sqrt{3} + 1\right)ft .</p>$