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Setler79 [48]
3 years ago
8

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

Mathematics
1 answer:
Marina CMI [18]3 years ago
3 0

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.

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