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 miles from island B. What bearing should he turn to, so he is heading straight towards island B?
1 answer:
We know that Applying the law of cosines: <span>c</span>²<span> = a</span>²<span> + b</span>²<span> - 2abcos(C) </span> <span>where: </span> <span>a,b and c are sides of the triangle and C is the angle opposite side c </span> <span>that is </span> <span>150</span>²<span> = 240</span>²<span> + 200</span>²<span> - 2(240)(200)cos(C) </span> <span>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>hence, </span> <span>he should turn in the direction of island b by 180 - 38.53 </span><span>= 141.47 degrees </span>
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