Question

NO LINKS!! Part 8a: Please help me with this problem

THIS IS NOT MULTIPLE CHOICE!!!

a. Through what angle should the captain turn to head directly to Barbados?

b. Once the turn is made, how long will it be before the ship reaches Barbados if the same 15-knot speed is maintained?
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Answer 1

26.38° (nearest hundredth)

30.7960166... hours = 30 hours 47 mins 37 secs

Explanation:

one knot = one nautical mile (nm) per hour

Therefore, 15-knot speed for 10 hours = 15 × 10 = 150 nm

Use cosine rule to find the distance between the ship and Barbados (blue dashed line on attached diagram).

Cosine rule: c² = a² + b² - 2ab cos(C)

Given:

• a = 150
• b = 600
• C = 20°

⇒ c² = 150² + 600² - 2(150)(600)cos(20°)

⇒ c² = 213355.3283...

⇒ c = 461.9040249... nm

Use sine rule to calculate smallest missing angle (red on attached diagram)

`\sf \implies (sin(A))/(150)=(sin(20))/(461.9040249)`

`\sf \implies sin(A)=(150sin(20))/(461.9040249)`

`\sf \implies A=6.376917848... \textdegree`

Sum of interior angles of a triangle = 180°

⇒ missing interior angle (green) = 180° - 20° - 6.376917848...° = 153.6230822...°

Angles on a straight line sum to 180°

⇒ x° = 180° - 153.6230822...° = 26.376917848...°

The distance between the Ship and Barbados is 461.9040249 nm

Therefore, to calculate the time, divide the distance by the speed:

t = 461.9040249... ÷ 15 = 30.7960166... hours