Question

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?

99 POINTS AVALIBLE

Answer 1

• AB=25
• BC=31

Apply Pythagorean theorem

`\\ \tt\hookrightarrow AC^2=AB^2+BC^2`

`\\ \tt\hookrightarrow AC^2=31^2+25^2`

`\\ \tt\hookrightarrow AC^2=961+625`

`\\ \tt\hookrightarrow AC^2=1586`

`\\ \tt\hookrightarrow AC=39.8mi`

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

Answer 2

16.18 miles could have been saved (nearest hundredth)

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.