The shortest distance between cache(final location of Madison in this case) and the water fountain( the starting point of Madison in this case) is given by: Option A: 34 yards
What is Pythagoras Theorem?
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
How are directions related?
East or west are perpendicular (forming 90° ) to north or south directions.
North is 180° to south, and east is 180 degrees to west.
For the given case, the below attached figure describes the path traveled by Madison.
- The point A is the water fountain in consideration,
- The point B is her turn for south direction
- The point C is the cache where she reached finally.
The shortest distance between her final and initial point is length of the line segment AC.
Using the Pythagoras theorem, we get the length of the line segment AC as:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\|AC| = \sqrt{|AB|^2 + |BC|^2}\\\\|AC| = \sqrt{30^2 + 16^2} = \sqrt{1156} = 34 \: \rm yards[/tex]
(positive sq. root since 'distance' is a non-negative quantity).
Thus, the shortest distance between cache(final location of Madison in this case) and the water fountain( the starting point of Madison in this case) is given by: Option A: 34 yards
Learn more about Pythagoras theorem here:
https://brainly.com/question/12105522
