Emergency landing. a plane leaves the airport in galisteo and flies 170 km at 68° east of north and then changes direction to fly 230 km at 48° 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 rescue crew will have to travel 329.46km, towards 18.99° south of east.

Explanation:

We just need to add the vectors of the different path that the plane took. We can use the component method, where descompose each vector in their x and y component and add the corresponding components:

Path 1:

Here, you need to keep in mind that the angle given is from the y-axis (north)

Path 2:

The angle is from the x-axis, but the vertical distance is toward south:

Summation:

As the y-component is negative, and the x-component positive, the rescue crew will have to move towards south of east.

Now, we use Pythagoras and trygonometry to find the magnitude and direction of the resulting vector:

18.99° south of east.