Island A is 150 miles from island B. A ship captain travels 240 miles from island A and then finds that he is off course and 200

Applying the cosine law, we can determine:

<span>c</span>²<span> = a</span>²<span> + b</span>²<span> - 2abcos(C) </span>
<span>where: </span>
<span>a, b, and c represent the sides of the triangle and C indicates the angle opposite to side c</span>

<span>Thus, we have:</span>
<span>150</span>²<span> = 240</span>²<span> + 200</span>²<span> - 2(240)(200)cos(C) </span>

<span>Now we solve for C</span>

<span>22,500 = 57,600 + 40,000 - 96,000cos(C) </span>
<span>22,500 - 57,600 - 40,000 = -96,000cos(C) 
</span>-75,100=-96,000cos (C)
cos (C)=0.7822916
C=arc cos(0.7822916)→ C=38.53°

<span>Therefore, the direction the captain should head towards island B is
180 - 38.53 </span><span>= 141.47 degrees</span>