Maths Made Easy Forums Standard Trigonometry Bearings – Non Right

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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

x2 = 2502 + 2002 – 2 × 250 × 200 × cos   70°

x2 = 68,297.99

x = 261 nautical miles

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• Sue leaves home and walks 15km on a bearing of 130°, arriving at point A. Jessica, her sister leaves home a little after Sue and also walks 15km but due to a compass error, arrives too far south and not far enough east, arriving a part B which is 1.5 km from point A. Which bearing did Jessica take?

$$\cos\theta=\frac{15^2+15^2-1.5^2}{2\times15\times15}$$

θ = 5.7º

∴ bearing = 130º + 5.7º

= 135.7°