Aplane leaves the airport in galisteo and flies 170 km at 68.0° east of north; then it changes direction to fly 230 km at 36.0° south of east, after which it makes an immediate emergency landing in a pasture. when the airport sends out a rescue crew, in which direction and how far should this crew fly to go directly to this plane?

The direction will be and the distance 250.75km.

Explanation:

Let's say A is the displacement vector which represents the first 170km and B the one for the next 230km. Then the components of these vector will be:

The vector which point from the origin to the final position of the plane will be R=A+B. We sum components on x and y independetly (vector property):

If is the direction of R then:

⇒ ⇒ .

The distance will be given by the magnitud of the vector R:

⇒ .