PreCalc bearing word problem

Question

You are the navigator for a flight from Minneapolis/St. Paul to Orlando. When the flight takes off, you are sent to take care of a problem in the passenger compartment. When you return 20 minutes later (20 minutes after takeoff) you realize the pilot has been flying at a bearing of S 37º E and should be flying at a bearing of S 12º E.

A. If it is 1300 miles from Minneapolis/St. Paul to Orlando and the plane travels at 300mph, at what bearing should the pilot turn to correct the course?

B. To what speed should the plane increase in order to arrive in Orlando on schedule?

C. If the plane flies at 30,000 feet, how many ground miles from Orlando should the plane start its decent in order to make a landing at an angle of 3.8º with the ground?

Answer 1

#A

a=100

b=?

c=1300

α=?

β=25°

γ=?

a^2+c^2-2ac(cosβ)=b^2

100^2+1300^2-2*100*1300(.906)=b^2

10000+1690000-2356400.246 =1464360^.5=1210.107=b

γ=acos((a^2+b^2-c^2))/(2ab)=153.144° Has to turn.=26.86°or 90-26.86+180=243.14°overall.