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## Homework Statement

## Homework Equations

A vector U=<x,y>

||U|| means the length of U = √(x^2 +y^2). vectors can also be written as U = ||U||(cosθi, sinθj)

## The Attempt at a Solution

so I start by naming the vectors.V is the direction the plane is now heading. V1 is the original direction of the plane. V2 is the direction of the wind.

V = V1 + V2

V1 = 600(cos148i+sin148j)

V2 = 80(cos45i+sin45j)

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 = <-452.7i + 374.5j>

To find the speed I found the length of vector V

||V|| = sqrt[ (-452.7)2+374.52] = 587.5 km/hr

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