we know that
The measurement of <u>the external angle</u> is the semi-difference of the arcs it includes.
In this problem
![21\°=\frac{1}{2}[arc\ RU-arc\ SU]](https://tex.z-dn.net/?f=21%5C%C2%B0%3D%5Cfrac%7B1%7D%7B2%7D%5Barc%5C%20RU-arc%5C%20SU%5D)
Solve for the measure of arc SU
![42\°=[arc\ RU-arc\ SU]](https://tex.z-dn.net/?f=42%5C%C2%B0%3D%5Barc%5C%20RU-arc%5C%20SU%5D)
therefore
the answer is
The measure of the arc SU is 
The correct answer per pound is $1.49 per pound. Kyle is correct because dividing 2.98/2= 1.49 or multiplying Kyle's answer by 2 will give you the correct amount!
Let us say that the intersection point of lines
AB and CD is called point E. The lines AB and CD are perpendicular to each
other which also means that the triangle CEB is a right triangle.
Where the line CB is the radius of the circle
while the side lengths are half of the whole line segment:
EB = 0.5 AB = 0.5 (8 ft) = 4 ft
CE = 0.5 CD = 0.5 (6 ft) = 3 ft
Now using the hypotenuse formula since the
triangle is right triangle, we can find for the radius or line CB:
CB^2 = EB^2 + CE^2
CB^2 = (4 ft)^2 + (3 ft)^2
CB^2 = 16 ft^2 + 9 ft^2
CB^2 = 25 ft^2
<span>CB = 5 ft = radius</span>
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>
