Newton is 4 kilometers due north of the airport, and Morristown is due east of the airport. If the distance between Newton and Morristown is 5 kilometers, how far is Morristown from the airport?
We can draw a diagram to visualize the problem:
N
|
4 km |
|____ A (airport)
5 km
M
From the diagram, we can see that we have a right triangle with N, A, and M as the three vertices. The distance between Morristown and the airport (AM) is the hypotenuse of the triangle.
To find AM, we can use the Pythagorean theorem:
AM^2 = AN^2 + NM^2
Substituting the given values, we get:
AM^2 = 4^2 + 5^2
AM^2 = 16 + 25
AM^2 = 41
Taking the square root of both sides, we get:
AM ≈ 6.40 km
Therefore, Morristown is approximately 6.40 kilometers from the airport.
To find the distance between Morristown and the airport, we can use the Pythagorean theorem since we have a right triangle formed by Newton, Morristown, and the airport.
Let's label the distance between Morristown and the airport as x kilometers.
Using the Pythagorean theorem, we can set up the following equation:
x^2 = 4^2 + 5^2
Simplifying, we have:
x^2 = 16 + 25
x^2 = 41
Taking the square root of both sides to solve for x, we get:
x = sqrt(41)
So, Morristown is approximately sqrt(41) kilometers away from the airport.