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Anne is 3m away from Ishan at a bearing of 100°. Katniss is 7m away from Anne at a bearing of 260°. By plotting the postitions Anne and Katniss ( using a scale of 1cm : 1m), estimate the distance of Katniss from Ishan.

Sagot :

Answer:

The distance of Katniss from Ishan is approximately 4.305 meters

Step-by-step explanation:

The distance between Anne and Ishan = 3 m

The bearing of Ann from Ishan = 100°

The distance between Anne and Katniss = 7 m

The bearing of Ann from Katniss = 260°

From the diagram of the bearing created with MS Word, let 'a' represent the distance between Ishan and Katniss, let 'b' represent the distance between Ishan and Anne and let 'c' represent the distance between Katniss and Anne, by cosine rule, we have;

b = 3 m

c = 7 m

∠A = 20°

a² = b² + c² - 2·b·c·cos(A)

a² = 3² + 7² - 2 × 3 × 7 × cos(20)

a = √(3² + 7² - 2 × 3 × 7 × cos(20)) ≈ 4.305

By calculation, the distance from Ishan to Katniss, a ≈ 4.305 m

By measurement on MS Word, the distance from Ishan to Katniss, a = √(1.783² + 3.976²) ≈ 4.357.

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