Island A is 210 miles from island B. A ship captain travels 230 miles from island A and then finds that he is off course and 180 miles from island B. What bearing should he turn to, so he is heading straight towards island B?

Let us assume a Triangle ABC. Where side AB is the distance of the island A and island B and is 210 miles. AC is the wrong Course that a ship took and is 230 miles. CB is the course straight towards island B from C and equals 180 miles.

Finding angle C:

Now that the three sides of the triangle are known, we can find the angle that the ship should turn to using the law of cosines:

Cos C = (a²+b²-c²)/2ab where c = AB, b = AC, a = BC

Cos C = (180² + 230² - 210²)/2*180*230

C = cos⁻¹ (41200/82800)

C = cos⁻¹ (0.4976)

angle C = 60.15

angle C = 60° approx

luketanderson0219 luketanderson0219 · Answer 2 · 2022-04-14T08:11:34+02:00

luketanderson0219 luketanderson0219

14-04-2022

Answer:

119.84

Step-by-step explanation:

Side a = 180

Side b = 230

Side c = 210

Angle ∠A = 48.03° = 48°1'49" = 0.83829 rad

Angle ∠B = 71.81° = 71°48'36" = 1.25332 rad

Angle ∠C = 60.16° = 60°9'35" = 1.04998 rad

180-60.16=119.84

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