Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the eastbound car has traveled 6 miles. If the two cars are now a straight-line distance of 10 miles apart, how far has the northbound car traveled? miles
Question
Two cars leave the same parking lot, with one heading north and the other heading east. After several minutes, the eastbound car has traveled 6 miles. If the two cars are now a straight-line distance of 10 miles apart, how far has the northbound car traveled? miles
Solution
This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, the straight-line distance between the two cars forms the hypotenuse, the distance traveled by the eastbound car forms one side, and the distance traveled by the northbound car forms the other side.
Given:
- The eastbound car has traveled 6 miles (one side of the triangle)
- The straight-line distance between the two cars is 10 miles (the hypotenuse)
We can set up the equation as follows:
(Length of the hypotenuse)^2 = (Length of one side)^2 + (Length of the other side)^2
Substituting the given values:
10^2 = 6^2 + (Distance traveled by the northbound car)^2
Solving for the distance traveled by the northbound car:
100 = 36 + (Distance traveled by the northbound car)^2
Subtract 36 from both sides:
64 = (Distance traveled by the northbound car)^2
Finally, take the square root of both sides to solve for the distance traveled by the northbound car:
8 = Distance traveled by the northbound car
So, the northbound car has traveled 8 miles.
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