You walk 34 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where you

You walk 34 m to the north, then turn 60° to your right and walk another 45 m. How far are you from where
you started and at what angle from east?

R² = P² + Q²+ 2PQ cos α and tan α = Q sin θ /( P + Q cos θ)

R² = 34² + 45²+ 2*34*45 cos 60
R = 68.63 m

tan α = 45 sin60 /( 34 + 45 cos 60)
α = 34.6° east of north.
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Or
In the north direction the net displacement is
34 + 45 cos 60 = 56.5 m

In the eastern direction his displacement is
45 sin 60 = 38.97 m

Net displacement is √ (56.5^2+ 38.97^2) = 68.64 N

tan θ = north displacement / east displacement =56.5 / 38.97
θ =55.4° north of east.
or 34.6° east of north .
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