Answer:
The distance from A to B is approximately 67.5 km
The bearing of B from A is approximately 86.89°
Explanation:
i) The distances and the bearing of the motion of the ship is given as follows;
The distance the ship sails on a bearing of 048° = 30 km
The distance further the ship sails on a bearing of 110° = 42 km
From the drawing of the sailing of the ship created with Microsoft Visio, we have;
∠C = 48° + 70° = 118°
By cosine rule, we have;
c² = b² + a² - 2·b·a·cos(∠C)
From which we have;
c² = 30² + 48² - 2 × 30 × 48 × cos(118°) ≈ 4,556.07810082
c ≈ √(4,556.07810082) ≈ 67.5
The distance from A to B = c ≈ 67.5 km
ii) By sine rule, we have;
a/sin(A) = b/sin(B) = c/sin(C)
∴ sin(A) = a·sin(C)/c
Substituting the values of the variables gives;
sin(A) ≈ 48·sin(118°)/67.5
∠A ≈ arcsin(48·sin(118°)/67.5) ≈ 38.89°
Therefore, the bearing of B from A ≈ 48 + 38.89 = 86.89°.