precal homework

Question

A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 645 mi/h, how far is she from her starting position?

Answer 1

According to Cosine law:

OA=(645 m/h)(1.5 h) AB=(645 m/h)(2.0 h) OB²=OA² + AB² - 2(OA)(AB)cos170⁰

Then OB≈2249 miles

Answer 2

Assume path is initially East. Finally at 645X1.5i+645X2X(unit vector in direction 10 degrees to south of East)

unit vector in direction 10 degrees to south of East=(cos10deg)i-(sin10deg)j

645X1.5i+645X2X((cos10deg)i-(sin10deg)j)

Final position is length of this vector

645X((1.5+2(cos10deg))i-(sin10deg)j)

Always assuming, as usual, that the earth is flat.