2 planes leave the airport at the same time. Minutes later plane A is 70 miles due north of the airport. Plane B is 168 miles due East of the airport. How far apart are the 2 airplanes.
?
I think 98 miles apart. Is that right?
Think of a right triangle. The airport is the vertex of the right angle. Plane A is 70 miles north (Straight up). Plane B is 168 miles East (Straight right). From plane A to B would be side C of the right triange.
C^2 = A^2 + B^2
C = sqrt (A^2 + B^2)
C = sqrt (70^2 + 168^2)
C = sqrt (33124)
C = 182 miles
Well, if we take into account that the two planes flew in different directions, we can't simply add the two distances together. Instead, we can use the Pythagorean theorem to find the distance between the two planes.
So, if we have one side that is 70 miles (plane A's distance from the airport) and another side that is 168 miles (plane B's distance from the airport), we can find the distance between the two planes by using the equation a^2 + b^2 = c^2.
In this case, it would be 70^2 + 168^2 = c^2.
After some quick math, we find that c^2 = 14924.
Taking the square root of that, we get c ≈ 122.07 miles.
So, the two planes are approximately 122.07 miles apart. Not 98 miles, but close!
To solve this problem, we can use the Pythagorean theorem, which 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 label the distance between the airport and plane A as A, and the distance between the airport and plane B as B.
We are given that the distance between plane A and the airport is 70 miles (A = 70), and the distance between plane B and the airport is 168 miles (B = 168).
We want to find the distance between the two planes, which is the hypotenuse of the right triangle formed by A and B.
Using the Pythagorean theorem, we have:
Distance between the two planes = √(A^2 + B^2)
= √(70^2 + 168^2)
= √(4900 + 28,224)
= √33,124
≈ 182.10 miles
Therefore, the two airplanes are approximately 182.10 miles apart, not 98 miles.
To find the distance between the two planes, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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.
In this case, the distance between the two planes forms a right-angled triangle, with one side being the 70 miles north and the other side being the 168 miles east. The distance between the two planes is the hypotenuse.
To solve for the distance between the two planes, you can use the formula:
Distance^2 = (North distance)^2 + (East distance)^2
Let's plug in the values:
Distance^2 = 70^2 + 168^2
Distance^2 = 4900 + 28224
Distance^2 = 33124
Now, find the square root of both sides to solve for the distance:
Distance = √33124
Distance ≈ 182
Therefore, the two planes are approximately 182 miles apart, not 98 miles apart.