Question

A sailing ship left harbour A and travelled 20km on a bearing of 125 degrees. It then changed course and sailed on a bearing of 035 degrees on a distance of 10km until it reached B. Calculate the distance between A and B. The bearing of A from B and the bearing of B from A.

Answer 1

To calculate the distance between points A and B, we can use the cosine rule. Let's label the points as follows: A is the starting point, B is the ending point, and C is the vertex of the triangle formed by the two sides and the line connecting A and B.

First, let's calculate the length of side AC using the given information:

Side AC = √(20^2 + 10^2 - 2 * 20 * 10 * cos(180° - (125° + 35°)))
= √(400 + 100 - 400 * cos(180° - 160°))
= √(400 + 100 - 400 * cos(20°))
≈ √(500 - 400 * 0.9397)
≈ √(500 - 375.88)
≈ √(124.12)
≈ 11.14 km

Now, let's calculate the bearing of A from B:

Angle A = 180° - (125° + 180° - 35°)
= 30°

Finally, let's calculate the bearing of B from A:

Angle B = 360° - Angle A
= 360° - 30°
= 330°

Therefore, the distance between A and B is approximately 11.14 km. The bearing of A from B is 30°, and the bearing of B from A is 330°.