A ship travels 240 miles due east and then makes a turn due south. It travels 320 miles south. How far is the ship from its starting point (shortest distance)?
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d = √( 240² +320²)= √160 000 = 400 miles
To find the shortest distance from the ship's starting point to its current position, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ship has traveled 240 miles due east and 320 miles due south. The distance traveled east acts as one side of the right triangle, and the distance traveled south acts as the other side.
To find the shortest distance, you need to find the hypotenuse, which represents the straight-line distance from the starting point to the ship's current position.
Using the Pythagorean theorem, the equation is:
(shortest distance)^2 = (240 miles)^2 + (320 miles)^2
(shortest distance)^2 = 57600 + 102400
(shortest distance)^2 = 160000
Taking the square root of both sides, we get:
shortest distance = sqrt(160000)
Using a calculator, you can find that the square root of 160000 is 400.
Therefore, the ship is 400 miles away from its starting point, in the shortest distance.