Answer:
58.7 km (nearest tenth)
Step-by-step explanation:
Bearing: The angle (in degrees) measured clockwise from north.
To find the distance between the shuttlecraft, model the scenario as a triangle and use the cosine rule to find the unknown side.
Cosine Rule
[tex]\sf c^2=a^2+b^2-2ab \cos C[/tex]
where:
- a, b and c are the sides of the triangle
- C is the angle opposite side c
Angle C is the included angle (the angle between two sides of a triangle).
⇒ ∠C = 62° - 30° = 32°
The two sides "a and b" are the side lengths of 100 km and 110 km.
The side c is the distance between the shuttlecraft (labelled x on the attached diagram).
Substitute the values into the formula and solve for x:
[tex]\implies \sf x^2=100^2+110^2-2(100)(110) \cos (32^{\circ})[/tex]
[tex]\sf \implies x^2=22100-22000\cos (32^{\circ})[/tex]
[tex]\sf \implies x=\sqrt{22100-22000\cos (32^{\circ})}[/tex]
[tex]\sf \implies x=58.67658719...[/tex]
Therefore, the shuttlecraft are 58.7 km apart (nearest tenth).
