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>
<h3>2
Answers: Angle 4 and angle 2</h3>
==================================================
Explanation:
Supplementary angles add to 180 degrees. Visually, supplementary angles can be glued together to form a straight angle or a straight line.
We see that happens with angles 1 and 4, and this also happens with angles 1 and 2. This is why these two angles make up the answer.
--------------
The other answer choices can be ruled out.
Angles 1 and 9 would be congruent if we knew the shallow sloping lines were parallel. The only time angles 1 and 9 are supplementary is if both are 90 degrees. In any other case, they are not supplementary angles.
Angles 1 and 12 are same side exterior angles. They would be supplementary if the shallow sloping lines were parallel. However, if you extend out each line, you'll see that they eventually intersect. Parallel lines never intersect.
The awnsey too this question is 1/12
