Step-by-step explanation:
a) To find the distance between the two balloons, you can use the cosine rule. Let's denote the distance between the balloons as \(d\), the distance traveled by Balloon A as \(a\), and the distance traveled by Balloon B as \(b\).
The cosine rule is given by:
\[ d^2 = a^2 + b^2 - 2ab \cos(C) \]
Here, \(C\) is the angle between the paths of the two balloons. The bearings given are with respect to the north, so the angle \(C\) is the absolute difference between the bearings.
\[ C = |29° - 43°| = 14° \]
Now, plug in the values into the cosine rule equation to find \(d\).
b) To determine the bearing Balloon A would have to travel to reach the position of Balloon B, you can use trigonometry. The bearing is essentially an angle measured clockwise from the north direction.
The angle \(D\) (clockwise from the north) that Balloon A would need to travel is found by:
\[ D = \text{Bearing of Balloon B} - \text{Angle between balloons} \]
\[ D = 43° - 14° \]
So, Balloon A would need to travel on a bearing of \(D\) to reach the position of Balloon B.
