Question

jennifer bikes 7 miles south and then turns to bike 13 miles east how far away is she from where she started?

Answer 1

Answer:

She is about 14.765 miles ($\sqrt{218}$ miles) from where she started

Step-by-step explanation:

There is a relation between the three sides of the right triangle

• The side opposite to the right angle is called hypotenuse and it is the longest side

• The other two sides called legs of the right angle

• The relation between them is: (hypotenuse)² = (leg1)² + (leg2)²

∵ Jennifer bikes 7 miles south

∵ She turns to bike 13 miles east

∵ South and East are perpendicular

→ That means the distance from her start point to end point represents

   a hypotenuse of a right triangle, whose legs are 7 and 13

∴  (hypotenuse)² =  (leg1)² + (leg2)², where

• hypotenuse is the distance between her start and end points

• leg1 is her distance in south direction

• leg2 is her distance in east direction

∵ Leg1 = 7 miles

∵ leg 2 = 13 miles

∴ (hypotenuse)² =  (7)² + (13)²

∴ (hypotenuse)² = 49 + 169

∴ (hypotenuse)² = 218

→ Take √  for both sides

∴ hypotenuse = $\sqrt{218}$

∴ hypotenuse ≅ 14.76482306

∴ She is about 14.765 miles ($\sqrt{218}$ miles) from where she started.