Two cars start from the same point driving in opposite directions. Both cars drive 6 miles. One car stops, the other car makes a 90° left-hand turn, and drive 8 miles. How far apart are the two cars now?
Round your answer to the nearest tenth of a mile. Enter the number only!
Make your sketch
Looks like you have a right-angled triangle with legs of 12 and 8
Use Pythagoras.
if the distance between them is x
x^2 = 12^2 + 8^2
finish it up
To find the distance between the two cars, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's represent the distance the first car traveled as x. Since both cars started from the same point and traveled in opposite directions, the second car also traveled a distance of x.
The first car traveled 6 miles, so its new position is 6 miles away from the starting point. The second car made a 90° left-hand turn and traveled 8 miles. This forms a right triangle with sides measuring 6 miles, 8 miles, and the distance between the two cars.
Using the Pythagorean theorem, we can solve for the distance between the two cars:
(distance between the two cars)^2 = (6 miles)^2 + (8 miles)^2
(distance between the two cars)^2 = 36 miles^2 + 64 miles^2
(distance between the two cars)^2 = 100 miles^2
Taking the square root of both sides, we find:
distance between the two cars = √(100 miles^2)
distance between the two cars = 10 miles
Therefore, the two cars are now 10 miles apart.