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After school, Tyler skateboards directly from school to a game store and then from the game store to a movie theater. The game store is 1212 kilometers south of the school and the movie theater is 55 kilometers east of the game store. What is the straight-line distance between the school and the movie theater?\newline____\_\_\_\_ kilometers

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Full solution

Q. After school, Tyler skateboards directly from school to a game store and then from the game store to a movie theater. The game store is 1212 kilometers south of the school and the movie theater is 55 kilometers east of the game store. What is the straight-line distance between the school and the movie theater?\newline____\_\_\_\_ kilometers
  1. Triangle Formation: Tyler's path forms a right triangle with the legs being the distances from the school to the game store and from the game store to the movie theater.
  2. Legs and Hypotenuse: Legs of the triangle: 12 km12\,\text{km} (south), 5 km5\,\text{km} (east). We need to find the hypotenuse.
  3. Pythagorean Theorem: Use the Pythagorean Theorem: a2+b2=c2a^2 + b^2 = c^2, where aa and bb are the legs and cc is the hypotenuse.
  4. Plug in Values: Plug in the values: 122+52=c212^2 + 5^2 = c^2.
  5. Calculate Sum: Calculate: 144+25=c2144 + 25 = c^2.
  6. Square Root Calculation: Add the values: 169=c2169 = c^2.
  7. Final Hypotenize: Take the square root of both sides: 169=c\sqrt{169} = c.
  8. Final Hypotenize: Take the square root of both sides: 169=c\sqrt{169} = c. Calculate the square root: c=13c = 13.

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