Answer
$2.7\ mi$
Work Step by Step
1. Use the figure given in the exercise, we have $\frac{sinA}{BC}=\frac{sinC}{8.4}$
2. With $A=24^\circ50'=24.8^\circ, B=47^\circ20'=47.3^\circ, C=180^\circ-47.3^\circ-24.8=107.9^\circ$
3. $BC=\frac{8.4sin24.8^\circ}{sin107.9^\circ}\approx3.7\ mi$
4. The height of the balloon is $h=BC\ sinB=3.7sin47.3^\circ\approx2.7\ mi$
