A woman leaves home and walks 5 miles west, then 3 miles southwest. In what direction must she walk to head directly home? (Round your answer to three decimal places.)

the answers are not 28.413 nor 61.587

She walks 59.003 degrees in north-east direction and this can be determined by using the Pythagorean theorem and trigonometric function.

Given :

A woman leaves home and walks 5 miles west, then 3 miles southwest.

The Pythagorean theorem can be used in order to determine the Hypotenuse.

Now, substitute the known terms in the above expression.

H = 5.83

Now, to determine the angle use the trigonometric function cosine.

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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°

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step-by-step explanation:

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