Answer: she would walk 59.003° north east.
Step-by-step explanation:
The direction of movement if the woman forms a right angle triangle. The distance due west represents the opposite side of the right angle triangle.
The distance due South west represents the adjacent side of the right angle triangle.
The distance that she walks back home(northeast) represents the hypotenuse of the right angle triangle.
To determine the hypotenuse, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
h² = 5² + 3² = 25 + 9 = 34
h = √34 = 5.83
Therefore, to determine θ, her direction home, we would apply
the cosine trigonometric ratio.
Cos θ, = adjacent side/hypotenuse. Therefore,
Cos θ = 3/5.83 = 0.515
θ = Cos^-1(0.515)
θ = 59.003°
