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QuestionFind the shortest distance between Stan and Wei, given Jeff's locations: 12 miles east of Stan and 16 miles north of Wei.

Studdy Solution

STEP 1

Assumptions1. Jeff lives12 miles east of Stan. . Jeff lives16 miles north of Wei.
3. We are looking for the shortest distance between Stan and Wei, which would be a straight line.

STEP 2

We can use the Pythagorean theorem to find the shortest distance between Stan and Wei. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written asc2=a2+b2c^2 = a^2 + b^2where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

STEP 3

In this case, the distance between Stan and Jeff (12 miles) and the distance between Jeff and Wei (16 miles) form the two sides of a right-angled triangle, and the distance between Stan and Wei is the hypotenuse. So we can write the equation asStanWei2=StanJeff2+JeffWei2StanWei^2 = StanJeff^2 + JeffWei^2

STEP 4

Substitute the given distances into the equation.
StanWei2=122+162StanWei^2 =12^2 +16^2

STEP 5

Calculate the squares of the given distances.
StanWei2=144+256StanWei^2 =144 +256

STEP 6

Add the squares of the distances.
StanWei2=400StanWei^2 =400

STEP 7

To find the length of the hypotenuse (the distance between Stan and Wei), we need to take the square root of both sides of the equation.
StanWei=400StanWei = \sqrt{400}

STEP 8

Calculate the square root of400.
StanWei=20StanWei =20So, the shortest distance that Stan and Wei can live from each other is20 miles.

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