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Bearings Trigonometry IGCSE/GCSE Mathematics 0580 Extended
{{DATE}}
Bearings Topic of Trigonometry IGCSE/GCSE Mathematics 0580 Extended
Question: A boy walks 6 km from a point P to a point Q on a bearing of 065°. He then walks to a point R a distance of 13 km, on a bearing of 146°. Calculate the distance from P to R to the nearest Km.
Solution: According to the given conditions, the figure is shown below.
After working on the figure
Here ∟ x=∟y (alternate angles)
∟Y = 65°
∟Z + 146°= 180°
∟Z = 34°
∟PQR = y + z = 65° + 34° = 99°
Applying cosine rule
PR² = 6² + 13² - 2 × 6 × 13 × cos99° = 229.4
PR = √229.4 = 15.12 = 15 km
Answer 15 km
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