Figure 1 shows 3 yachts A, B and C which are assumed to be in the same horizontal plane - Edexcel - A-Level Maths Pure - Question 7 - 2008 - Paper 2

To find the distance between yachts B and C, we can use the cosine rule in triangle ABC.

Let ( AC ) be the distance between A and C, which is 700 m. The angle at A is found to be 15° (from the bearing provided). Therefore, the angle at C can be calculated as follows:

1. Find the angle at B: ( 180° - 15° - 90° = 75° ).

Now we can use the cosine rule:

$BC^2 = AB^2 + AC^2 - 2 \cdot AB \cdot AC \cdot \cos(B)$

Where ( AB = 500 ) m, ( AC = 700 ) m, and ( B = 75° ).

Calculating:

$BC^2 = 500^2 + 700^2 - 2 \cdot 500 \cdot 700 \cdot \cos(75°)$
$BC^2 = 250000 + 490000 - 700000 \cdot 0.2588$
$BC^2 = 740000 - 181160$
$BC^2 = 558840$
$BC = \sqrt{558840} ≈ 747.87 m$

Therefore, the distance between yacht B and yacht C to 3 significant figures is approximately 748 m.