I'm trying to do this homework problem but I keep getting an answer that is not given. Can someone tell me what I am doing wrong please. This is for University level calc 3.

so I start by naming the vectors.

**V** is the direction the plane is now heading.

**V**_{1} is the original direction of the plane.

**V**_{2 }is the direction of the wind.

**V** =

**V**_{1} +

**V**_{2 }**V**_{1} = 600(cos148

**i**+sin148

**j**)

**V**_{2} = 80(cos45

**i**+sin45

**j**)

next I distributed, combined like terms and factored out

**i** and

**j** **V** = (600cos148+80cos45)

**i** + (600sin148+80cos45)

**j**
I plugged that into my calculator and got

**V** = <-452.7

**i** + 374.5

**j**>

To find the speed I found the length of vector

**V**
||

**V**|| = sqrt[ (-452.7)

^{2}+374.5

^{2}] = 587.5 km/hr

That isn't one of the options.. am i wrong"?