Sailor's Wind Speed: 5.4mph East & 13.4mph SW/NE

[physics2hard]

A sailboat is sailing due east at 5.40 mph. The wind appears to blow from the southwest at 13.4 mph.

1. What is the true wind speed?
2.What is the true wind direction? ( south of west).
3.What is the true wind speed if the wind appears to blow from the northeast at 13.4 mph?
4.What is the true wind direction ( north of east) if the wind appears to blow from the northeast at 13.4 mph?

I tried solving the first question but did not get the correct answer. I know if you get the first question right it is easy to solve the second. Here's what I tried

sqrt ((13.4*sqrt (2)- 5.4)^2 + (13.4* sqrt(2))^2))= 23.29 mph but it wasn't right
this is Ax part this is Ay part

after finding the Ax and Ay just plug into equation:
theta=arctan(Ax/Ay)

PLEASE HELP ASAP NEED BY TONIGHT!

 

[tiny-tim]

Welcome to PF!

Hi physics2hard! Welcome to PF!

(have a square-root: √ )

sqrt ((13.4*sqrt (2)- 5.4)^2 + (13.4* sqrt(2))^2))= 23.29 mph

erm … cos45º = 1/√2, isn't it?

(and check your minus sign)