A plane flies from Mascot Airport on a bearing of 050° at 500 knots. Another plane leaves Mascot Airport at the same time and flies on a bearing of 120° at 400 knots. (1 knot = 1 nautical mile per hour)
a. Copy and complete the information on a diagram.
b. How far apart will the planes be after 30 minutes, correct to the nearest nautical mile?
a.
b. 30 minutes is half an hour, so the first distance ½ × 500 = 250 nautical miles
the second distance ½ × 400 = 200 nautical miles
the first bearing is 50° and the second bearing is 120°, leaving the angle in between them as 120° – 50° = 70°
since we have two sides and the included angle, will be using the cos rule
x^{2} = 250^{2} + 200^{2} – 2 × 250 × 200 × cos 70°
x^{2} = 68,297.99
x = 261 nautical miles