Island A is 150 miles from Island B. A ship captain travels 310 miles from Island A and then finds that he is off course and 200 miles from Island B. What angle, in degrees, must he turn through to head straight for Island B?

156.37°

Step-by-step explanation:

We solve this above question, using Cosine rule which is given as:

Cos C = a² + b² - c²/2ab

Let the Angle be represented as: x

Cos x = 310² + 200² - 150²/2 × 310 × 200

x = arc cos [ 310² + 200² - 150²/2 × 310 × 200]

x = 23.63°

The angle, in degrees, that he must turn through to head straight for Island B is given as:

180° - 23.63°

= 156.37°

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