joey and helen are standing in opposite corners of a rectangular field. if the field has dimensions 120ft by 209 ft, how far apart are they?
Please help me solve this and lead me through the problem , thank you. :)
This calls for the Pythagorean Theorem.
a^2 + b^2 = c^2
120^2 + 209^2 = c^2
14,400 + 43,681 = c^2
58,081 = c^2
241 = c
Thank you so much for explaining Mrs. Sue :).
You're welcome.
To find the distance between Joey and Helen, 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, Joey and Helen are standing at opposite corners of a rectangular field, which can be visualized as the two shorter sides of a right triangle. The longer side of the triangle represents the distance between them.
First, let's label the sides of the triangle:
- The length of the field (or the longer side of the rectangle) is 209 ft, which will be one of the legs of the right triangle.
- The width of the field (or the shorter side of the rectangle) is 120 ft, which will be the other leg of the right triangle.
To find the length of the hypotenuse (the distance between Joey and Helen):
1. Substitute the lengths of the two legs into the Pythagorean theorem equation: a^2 + b^2 = c^2. Here, a = 209 ft and b = 120 ft.
209^2 + 120^2 = c^2
43681 + 14400 = c^2
58081 = c^2
2. Solve for c, the length of the hypotenuse, by taking the square root of both sides of the equation:
√58081 = √c^2
240.9 ≈ c
Hence, Joey and Helen are approximately 240.9 ft apart from each other.