Question

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?

Answer 1

Answer:

He should turn 60° to head straight towards island B.

Step-by-step explanation:

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