The pilot of a plane leaves the airport at a heading of 030° for 200 miles, then changes course to 128° for the
next 400 miles. What is the true bearing for the captain to return to the airport?
о
а
028°
010°
100

  280°

Step-by-step explanation:

We can use the law of cosines to find the distance back to the airport. The internal angle at the first turning point is ...

  180° -(128° -30°) = 82°

The law of cosines tells us ...

  a^2 = b^2 +c^2 -2bc·cos(A)

  a^2 = 200^2 +400^2 -2·200·400·cos(82°) ≈ 177,732.3

so the distance home is ...

  a ≈ √177,732.3 ≈ 421.58 . . . . miles

Now, the law of sines can be used to find the internal angle at C.

  sin(C)/c = sin(A)/a

  C = arcsin(c/a·sin(A)) = arcsin(400/421.58·sin(82°)) ≈ arcsin(0.939571)

  C ≈ 69.98°

This angle, added to the original bearing of 30° is 99.98°, which is the opposite of the bearing home. That must be 180° +99.98° = 279.98°.

The true bearing for return to the airport is 280°.

1/800 is the right answer

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