Solution

1. To find c: c²=a²+b²-(2abCosc)

c²=300²+100²-(2(300)(100)Cosc)

c²=90000+10000-(60000(-0.2588))

c²=100000+15529.1427

c²=115529.1427

c=339.90 ft.

2. To find ÐA: Sin A = Sin 105

300 339.90

ÐA: 339.90(Sin A)=300(Sin 105)

Sin A =300(Sin 105)

339.90

mÐA=Sin^-1((300(Sin 105))

339.90)

mÐA=58.5^o

3. To find ÐC: 180^o-58.5^o

ÐC=121.5^o

4. To find c: c²=a²=b²-(2abCosc)

c²=339.90²+1290²-(2(339.90)(1290)(Cos 121.5)

c²=115532.01+1664100-(876942(Cos 121.5))

c²=1779632.01+458200.9363

c²=2237832.946

c=1495.94

Does the plane have enough fuel to make it to Bojanglia from the drop off point?

From Australia to Drop off point=1290 mi.

From Drop off point to Bojanglia=339.90 mi.

Total trip=1629.9 mi.

Plane gets 85 mpg of fuel, holds 20 gallons=1700 miles

Yes, the plane has enough fuel to make it to the drop off point.

Will the troops rescue the sloth and make it to Bojanglia in less than three hours?

From drop off point to Pyramid=100 mi.

From pyramid to Bojanglia=300 mi.

Total trip=400 mi.

Kangaroos travel 145 mph

~Takes 10 minutes to rescue the sloth from the pyramid

400/145=2.76 hours=165.6 minutes+10minutes (to rescue the sloth)=175.6 minutes/60=2.93 hours

The troops have enough time to rescue the sloth and make it back to the plane.

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