Answer:
The bearing of the balloon from its starting point = N 71.9° E
Step-by-step explanation:
To find the distance to the starting point, the wind and the height are perpendicular to each other. So, use the Pythagorean Theorem :
(Distance from the starting point)² = 8.25² + 6.00² = 112.56
⇒ Distance = 10.6 miles
Then to determine the bearing y :
[tex]\tan x=\frac{ opposite}{adjacent}\\\\Therefore, \tan x = \frac{6}{8.25} = 0.6857\\\\\implies x = \tan^{-1} (0.6857) ={34.4}^{\circ}[/tex]
Since the original bearing that the balloon set off at was N 37.5° E,
⇒ y = 37.5° + 34.4°
= 71.9°
Hence, The bearing of the balloon from its starting point = N 71.9° E
