#### Answer

Total height of Mt. Everest = T = 29,003.8 ft

#### Work Step by Step

To start, we break down what we know, and what we need to find.
Things we know:
Altitude = s = 14,545 ft
Straight-line distance = h = 27.0134 miles
h (in feet) = 27.0134 miles $\times$ 5,280 $\frac{feet}{miles}$ = 142,631 ft
angle u = $\theta$ = 5.82$^{\circ}$
Things we need to find:
Partial height of Mt. Everest = P
Total height of Mt. Everest = T = P + s
To find the partial height, P, of Mt. Everest, we can assume that the straight-line distance, h, is the hypotenuse in a triangle with angle, u.
Therefore:
$\sin\theta$ = $\frac{P}{h}$
$\sin5.82^{\circ}$ = $\frac{P}{142,631}$
P = $142,631\times\sin5.82^{\circ}$
P = 14,463.3 ft
T = 14,463.3 + 14,545.0
T = 29,003.8 ft