Step-by-Step Solution
Key Concept: Apply tangent ratios in two right triangles sharing a common height to find the total distance.
In $\triangle ABE$, $\tan 30° = \frac{h}{x}$, so $h = 100\sqrt{3}$ ft (equation 1). In $\triangle ABD$, $\tan 45° = \frac{h}{H} = 300$ ft (equation 2). Since $\frac{h}{\tan 30°} = \frac{h}{1/\sqrt{3}} = h\sqrt{3} = 300 + x$, and $h\sqrt{3} = 300 + x$ using equations (1) and (2), we get $x = 150(\sqrt{3}+1)$ ft.
Correct Answer: 150(√3+1)