A person leaves her home and walks 330 feet due north, then she walks 640 feet east, then she walks 900 feet north and 370 feet east. How far, to the nearest tenth of a foot, is she from her starting point?
total N = 330 + 900 = 1230
Total E = 640 + 370 = 1010
so
sqrt (1230^2 + 1010^2)
To find out how far the person is from her starting point, we can use the Pythagorean theorem. The Pythagorean theorem 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, we can consider the person's starting point as the origin of a coordinate system. The person walks 330 feet due north, so we can consider this as moving "up" 330 feet on the vertical axis. Then, the person walks 640 feet east, which is equivalent to moving "right" 640 feet on the horizontal axis. Next, the person walks 900 feet north (up) and 370 feet east (right).
We can plot these movements on a graph as follows:
330 feet north = a point on the vertical axis at (0, 330)
640 feet east = a point on the horizontal axis at (640, 0)
900 feet north + 370 feet east = a point in the first quadrant at (370, 1230)
Now, we can calculate the distance from the origin (starting point) to this final point using the Pythagorean theorem.
The horizontal distance (x-axis) is 370 feet, and the vertical distance (y-axis) is 1230 feet.
Using the Pythagorean theorem:
Distance = √(370^2 + 1230^2)
= √(136900 + 1512900)
= √1659800
≈ 1287.1 feet (rounded to the nearest tenth)
Therefore, the person is approximately 1287.1 feet away from her starting point.