Question

Stacy is playing hide-and-seek with Austin and Christopher. Austin is hiding 12 meters south of Stacy, and Christopher is hiding 5 meters east of Austin. How far apart are Stacy and Christopher?

Answer 1

Stacy is 13 meters apart from Christopher.

Explanation:

Given:

Austin is hiding 12 meters south of Stacy.

Christopher is hiding 5 meters east of Austin.

To find distance between Stacy and Christopher.

Solution:

From the given data, we will trace the positions of each as shown in the figure below.

We find that the distance between Stacy and Christopher is the hypotenuse side of a right triangle formed by their positions.

By Pythagorean theorem:

`Hypotenuse^2=Leg1^2+Leg2^2`

From the triangle:

Leg 1 = 5 meters

Leg 2= 12 meters

Plugging in the values.

`Hypotenuse^2=5^2+12^2`

Simplifying.

`Hypotenuse^2=25+144`

`Hypotenuse^2=169`

Taking square root both sides.

`√(Hypotenuse^2)=√(169)`

`Hypotenuse=13` meters

Thus, distance between Stacy and Christopher = 13 meters