How Can You Determine the Third Leg of a Sailor's Voyage Using Vector Addition?

[joe215]

Homework Statement

A sailor in a small sailboat sails 2km east, then 3.4 km NE, then an additional distance in an unknown direction. Her final position is 6.68 km directly east of her starting point. Find the magnitude and direction of the third leg of her voyage.

The Attempt at a Solution

I've drawn a diagram, but I honestly don't know where to start to find the third leg of the voyage. This one is really stumping me.

Thanks!

 

[HallsofIvy]

1. Draw a line from some starting point, A, to the right (East) 2 cm (representing 2 km) long. Call the endpoint B.

2. From B, draw a second line slanting 45 degrees up (NE) 3.4 cm long (representing 3.4 km). Call the endpoint C.

3. Go back to A and draw a line to the right (same as (1)) 6.68 cm long. That line should go right over B and exend 6.68- 2.0= 4.68 cm farther. call the end point D.

4. Draw a line from C to D. That is the "third leg". You should be able to determine its angle and length from the triangel BCD.