An airplane flies from City A in a straight line to City B, which is 70 kilometers north and 140 kilometers west of City A. How far does the plane fly?
An airplane flies from City A in a straight line to City B, which is 60 kilometers north and 180 kilometers west of City A. How far dos the plane fly? (Round your answer to the nearest
kilometer.)
km
Well, let's consider this. The airplane is traveling in a straight line from City A to City B, which means it's not doing any fancy zig-zagging or loop-the-loops. So, we can simply use the good old Pythagorean theorem to find the distance.
Now, according to my calculations, if the airplane flew 70 kilometers north and 140 kilometers west, it's essentially forming a right-angled triangle. So, we just need to find the hypotenuse of this triangle.
Using the theorem, a^2 + b^2 = c^2, where a and b are the lengths of the two legs and c is the length of the hypotenuse, we can plug in the values. So, (70^2) + (140^2) = c^2.
After some math magic, we find that c^2 = 4900 + 19600, giving us c^2 = 24500. Taking the square root of both sides, we get c ≈ 156.47 kilometers.
So, the plane flies approximately 156.47 kilometers. Although, that's assuming it didn't make any unexpected detours to pick up snacks along the way!
To find out how far the airplane flies, we can use 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 other two sides.
In this case, the airplane's path forms a right triangle with sides of length 70 kilometers (north) and 140 kilometers (west). We can consider the north side as the vertical side (which we'll call the "y-axis") and the west side as the horizontal side (which we'll call the "x-axis").
Using the Pythagorean theorem, we can calculate the length of the hypotenuse (the airplane's path):
Hypotenuse^2 = Vertical side^2 + Horizontal side^2
Hypotenuse^2 = 70^2 + 140^2
Hypotenuse^2 = 4900 + 19600
Hypotenuse^2 = 24500
Hypotenuse ≈ √24500
Hypotenuse ≈ 156.62 kilometers
Therefore, the airplane flies approximately 156.62 kilometers.
This looks like a problem for Pythagoras.
a^2 + b^2 = c^2
70^2 + 140^2 = c^2
4,900 + 19,600 = c^2
24,500 = c^2
156.52 = c