Answer
$(a)$ See the image below.
$(b)$ Approximately $66.67 ft.$
Work Step by Step
$(a)$ See the image above.
$(b)$ To calculate the height, we have to write and calculate:
$\sqrt{1.5x+(\frac{x}{5280})^2}=10$
For easier way, we can use the graph. We need to find intersection of the graph at $y=10$. That is point $A(66.67, 10)$
Height has to be approximately $66.67 ft.$