Pre-calculus

An expedition walks 4 kilometers from camp on a bearing of 30 degrees, then turns and walks 10 km on a bearing of 160 degrees. Find the magnitude of the new location relative to the beginning location using vectors.

-> if you can, can you possibly show how the triangle would look like along with how to solve it using vectors/ vector formula.
-> here's what I have so far: v1=4(cos60, sin60), v2=10(cos70, -sin70), v1+v2=vr, ||vr||=sqrt of vectors^2 from vr

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  1. Disp. = 4km[30o] + 10km[160o].

    X = 4*Cos30 + 10*Cos160 = -5.93km.
    Y = 4*sin30 + 10*sin160 = 5.42km.

    Tan A = Y/X = 5.42/(-5.93) = -0.91403, A = -42.43o N. of W.137.6o CCW from + x-axis.

    Disp. = X/Cos A = (-5.93)/Cos137.6 = 8.03 km[137.6]

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