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? milesSubmit

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 of a right triangle, while the distances each car has traveled form the other two sides.

We know that the eastbound car has traveled 6 miles (one side of the triangle) and the straight-line distance between the two cars is 10 miles (the hypotenuse). We can let x be the distance the northbound car has traveled (the other side of the triangle).

According to the Pythagorean theorem, we have:

(6 miles)^2 + x^2 = (10 miles)^2

Solving for x gives us the distance the northbound car has traveled:

x^2 = (10 miles)^2 - (6 miles)^2 x^2 = 100 miles^2 - 36 miles^2 x^2 = 64 miles^2 x = sqrt(64 miles^2) x = 8 miles

So, the northbound car has traveled 8 miles.

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 of a right triangle, and the distances each car has traveled form the other two sides.

Let's denote:

• the distance the eastbound car has traveled as a = 6 miles,
• the straight-line distance between the two cars as c = 10 miles,
• the distance the northbound car has traveled as b (which we're trying to find).

According to the Pythagorean theorem, we have:

a² + b² = c²

Substituting the known values, we get:

6² + b² = 10²

Solving this equation for b gives:

b² = 10² - 6² b² = 100 - 36 b² = 64

Taking the square root of both sides gives:

b = √64 b = 8

So, the northbound car has traveled 8 miles.