Aship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. find the distance of the end of the trip from the starting point, to the nearest kilometer.

To solve this problem you need to draw a picture of 2 trajectories and find the angle between them. After you calculate the angle between them, you use cosine theorem to determine distance from starting to ending point. 

In this case, the angle between 2 trajectories is exactly 90 degrees, so therefore we can use Pythagoras theorem (you will get the same result using cosine theorem):



answer is 159 km

 draw the figure from figure you have rightangle triangle so by 
using Pythagoras' theorem we have: 

d² = 84² + 135² 
 =25281 

d = √25281 
 d = 159 km 
see the attachment below
hope it helps