a plane travels 150 miles, at a heading north west 42 degrees. changes derection and travels 105 miles at a he

Question

ading 52 degrees. how far is the plane from it's original position?

Answer 1

"Heading" confuses me, because I don't know what it means. I assume you mean the plane went 150 miles in a direction 42 degrees west of north, then 105 miles in a direction 52 degrees west of north. In other words, when he changed course, he went 10 more degrees toward the west.

If that's right, then he ended up

150 cos 42 + 105 cos 52 = 176.1 miles north of his starting position, and

150 sin 42 + 105 sin 52 = 183.1 miles west of the starting position.

Putting them together, he ended up

sqrt(176.1^2 + 183.1^2) = sqrt(64546) = 254 miles from his starting position. (Answer)

Because that course change was so slight -- only ten degrees -- it's almost like he traveled in a straight line. He flew 255 miles total, and ended up 254 miles away. The course change only cost him one mile in total distance.