JOhn and Jason are standing 12 feet apart. Julie is standing 31 degrees NW of Jason. John is standing 49 degrees SW of Julie. can you uniquely determine how they stand with respect to each other? on what basis?
I don't think you have enough information.
I started by placing Jason
Draw a vertical from Jason than Julie is 31° W of that.
Place Julie anywhere an that line
Draw a vertical at Julie
Draw a line 49° W of that vertical to place John who is anywhere on that line
Join the line between Jason and John, label it 12 feet
Now the line between the verticals of Jason and Julie is a transversal between parallel lines, so the angle formed at Julie is 31+49 or 80°
So in the triangle you only have one angle and one side, which is not enough to determine the triangle
so do you think the answer is no, that in the triangle there is only one angle and one side which is not enough to determine the triangle?
Yes, we can determine how they stand with respect to each other based on the given information.
First, let's draw a diagram to visualize their positions:
```plaintext
J (John)
/
/
/
J (Julie)
\
\
\
J (Jason)
```
Now, we know the following information:
1. John and Jason are standing 12 feet apart.
2. Julie is standing 31 degrees northwest (NW) of Jason.
3. John is standing 49 degrees southwest (SW) of Julie.
To determine their positions, we can start by placing Jason as our reference point at the center:
```plaintext
J (Julie)
/ \
/ \
J (Jason)----------J (John)
```
Next, we know that Julie is standing 31 degrees northwest of Jason. This means we need to draw a line 31 degrees to the northwest (compass direction) from Jason:
```plaintext
J (Julie)
/ \
/ \
J (Jason)---------J (John)
|
|
|
```
Finally, John is standing 49 degrees southwest of Julie. So, we need to draw a line 49 degrees to the southwest (compass direction) from Julie:
```plaintext
J (Julie)
/ \
/ \
J (Jason)---------J (John)
|
|
J (John)
```
Now, we can see how they stand with respect to each other. Jason is between Julie and John, and they are all connected in a triangular shape.
Therefore, based on the given information, we can determine their positions relative to each other.