Jay, Kay, Ray found themselves far apart for lunch while working in a field. Jay could see Kay, then turned 75 degrees and see Ray. Kay could see Ray, then turn 51 degrees and see Jay. Ray could see jay, then turn 54 degrees and see Kay. Which two were the furthest apart?

A) Ray and Jay
B) Kay and Ray
C) jay and Kay
D) Kay and Ray were the same distance as Ray and Jay

I believe the answer is A but can someone please check this for me and if I made a mistake can someone please explain to me why I got it wrong

I suspect it makes a difference which direction each one turns.

To determine which two individuals were the furthest apart, we need to compare the angles they turn. Since we are given the angles turned by each person, we can use trigonometry to find the distances.

Let's first assume that the field they are working in is flat. From Jay's perspective, he sees Kay first and then turns 75 degrees to see Ray. Similarly, Kay sees Ray and turns 51 degrees to see Jay, while Ray sees Jay and turns 54 degrees to see Kay.

Now, let's label the distance between Jay and Kay as d1 and the distance between Jay and Ray as d2.

To find d1, we can use the Law of Sines:
d1 / sin(75°) = d2 / sin(51°)

To find d2, we can use the Law of Sines again:
d2 / sin(75°) = d1 / sin(54°)

From these two equations, we can solve for d1 and d2. By calculating these distances, we can determine which two individuals were the furthest apart.

Given the information provided, we can now calculate the distances and determine the answer.