Trigonometric question?

Question

A plane flies 810 miles from A to B with a bearing of N 75 E. Then it flies 648 miles from B to C with a bearing of N 32 E. Find the straight line distance and bearing from A to C. The bearing are in degrees. Tell me also the measure of the three angles inside the triangle formed, and how you got it. Thank you.

Answer 1

Young Dro

Answer 2

You have to draw out the triangle to solve this. The first step is to find the angle ABC - This is (180-75) + 32= 137
Next Next you use the trig formula
c**2 = a**2 +b**2 - 2.a.b.cos(Theta) where ** is square and Theta is the angle between sides b and c
In this case theta is 137, a=810, b=648 so you should be able to get c
you can then use the same formula to get find the angle CAB. Once CAB is known, bearing from A to C is 75 - this angle.

Answer 3

here is what i get

AC = b
AB = c
BC = a

b^2 = c^2 + a^2 - 2ac(cos(B))
b^2 = 810^2 + 648^2 - 2(810 * 648)cos(32)
b^2 = 656100 + 419904 - 2(524880)cos(32)
b^2 = 1076005 - 1049760cos(32)

c = 944

if you add 32 and 75 and then subtract from 180, you get

73

ANS :

944 miles at 73°