Answer
15.3 mi, N 89.1° E
Work Step by Step
We know distance travelled = speed X time
In triangle ABC,
$AB = 9.5 mi/hr \times 1 hr = 9.5\ mi$
$BC = 8 mi/hr \times 1.5 hr = 12\ mi$
$\angle B = 37.5^{\circ} + 52.5° = 90°$
To find final distance of balloon from starting point i.e length of segment AC
Using Pythagoras theorem
$AC = \sqrt{AB^2 + BC^2} = \sqrt{9.5^2 + 12^2} = 15.3\ mi$
Finding bearing
In triangle ABC
$\tan A = \frac{BC}{AB} = \frac{12}{9.5} = 1.2631$
$\angle A = \tan^{-1} (1.2631) = 51.631°$
Bearing of C from A $= (51.6° + 37.5°) = N\ 89.1° E$
