T is a radar tower - OCR - GCSE Maths - Question 17 - 2019 - Paper 6

To find the distance between aircraft A and aircraft B at 3pm, we use the cosine rule. Let:

• a = distance from T to A = 3250 km
• b = distance from T to B = 4960 km
• θ = angle between the bearings, calculated as:

$heta = 57° - 15° = 42°$

According to the cosine rule:

$c^2 = a^2 + b^2 - 2ab \cos(θ)$

Substituting the values:

$c^2 = 3250^2 + 4960^2 - 2 \times 3250 \times 4960 \times \cos(42°)$

Calculating:

$c^2 = 10562500 + 24601600 - 2 \times 3250 \times 4960 \times 0.8390$

$c^2 = 35164100 - 5328312.16$

ightarrow c ≈ 5463.4 ext{ km}$$ Therefore, the distance between aircraft A and B at 3pm is approximately 5463.4 km.