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To avoid a large, shallow reef, a ship set a course from point A and traveled 25 miles east to point B. The ship then turned and traveled 31 miles south to point C. If the ship could have traveled in a straight line from point A to point C, about how many miles could it have saved?
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semsee45

Answer:

16.18 miles could have been saved (nearest hundredth)

Step-by-step explanation:

Distance of original journey = 25 + 31 = 56 miles

Using Pythagoras' Theorem to calculate distance AC:

    a² + b² = c²

⇒ 25² + 31² = AC²

⇒ 1586 = AC²

⇒ AC = 39.82461... miles

Difference = 56 - 39.82461 = 16.17538... miles

Therefore, 16.18 miles could have been saved.

Ver imagen semsee45
  • AB=25
  • BC=31

Apply Pythagorean theorem

[tex]\\ \tt\hookrightarrow AC^2=AB^2+BC^2[/tex]

[tex]\\ \tt\hookrightarrow AC^2=31^2+25^2[/tex]

[tex]\\ \tt\hookrightarrow AC^2=961+625[/tex]

[tex]\\ \tt\hookrightarrow AC^2=1586[/tex]

[tex]\\ \tt\hookrightarrow AC=39.8mi[/tex]

  • Total distance=25+31=56mi
  • Distance could saved=56-39.8=16.2mi
Ver imagen Аноним

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