rachel drives 33 miles east and then drives 56 miles north. how far is she from her starting point?
just another Pythagorean Theorem problem ...
To find out how far Rachel 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, Rachel has traveled 33 miles east and 56 miles north, forming a right triangle. The distance from her starting point to her current position is the hypotenuse of this right triangle.
Using the Pythagorean theorem, we can calculate the distance as follows:
- Square the distance traveled east: 33^2 = 1089
- Square the distance traveled north: 56^2 = 3136
- Sum the two squared distances: 1089 + 3136 = 4225
- Take the square root of the sum: √4225 = 65
Therefore, Rachel is approximately 65 miles from her starting point.
To find the distance Rachel is from her starting point, we can use the Pythagorean theorem.
Let's assume Rachel's starting point is the origin (0,0) on a coordinate plane.
Rachel drives 33 miles east, which means she moves 33 units to the right on the x-axis. This brings her to the point (33,0).
Then, she drives 56 miles north, which means she moves 56 units up on the y-axis. This brings her to the point (33, 56).
Using the Pythagorean theorem, we can calculate the distance between these two points:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, x1 = 0, y1 = 0, x2 = 33, and y2 = 56:
Distance = √((33 - 0)^2 + (56 - 0)^2)
Distance = √(33^2 + 56^2)
Distance = √(1089 + 3136)
Distance = √4225
Distance = 65
Therefore, she is 65 miles away from her starting point.