Answer
8828 ft
Work Step by Step
Draw a sketch (see below). Observe the right triangle.
So, $\theta=26^{\circ}$
$\displaystyle \tan 26^{o}=\frac{a}{b},\quad$ solve for a:
a$=14.000\cdot\tan 26^{o}\approx$6828.25623992
$\approx$ 6828 ft above the cabin, which is at 2000 ft .
In total, the altitude is 6828+2000 = 8828 ft
.