Jim was told by his grandfather that he buried a time capsule when he was a kid. The grandfather gave the map to Jim and asked him to find it. The map directs Jim to start from the tallest tree in the town. It says the following;

Question

Jim was told by his grandfather that he buried a time capsule when he was a kid. The grandfather gave the map to Jim and asked him to find it. The map directs Jim to start from the tallest tree in the town. It says the following;

"From the tree, walk 13m to the South."
"Then turn 90° and walk 11m."
"Then turn 90° again and walk 9m."
For each of the four possible locations of the treasure, give the distance from the tree and the direction, expressed as an angle measured counterclockwise from east. List the possible locations in counterclockwise (CCW) order, starting with the one which is closest to due west.

Answer 1

1. 9 m @ 90 Deg.

2. 11 m @ 180 Deg.

3. 13 m @ 270 Deg.

Your prob. says 4 possible locations, but I only see 3.

Answer 2

To solve this problem, we need to follow the instructions given in the map step by step. Here's how we can find the possible locations of the treasure:

1. Start from the tallest tree in the town.
2. Walk 13m to the South.
3. Turn 90° counterclockwise (to the left) and walk 11m.
4. Turn 90° counterclockwise again and walk 9m.

Now, let's calculate the distances and directions for each of the four possible locations:

1. Option 1: Walk 13m South, then turn left and walk 11m (west), followed by another left turn and walk 9m north.
Distance from the tree: 13m - 9m = 4m (south)
Direction: Counterclockwise (CCW) angle from east = 270°

2. Option 2: Walk 13m South, then turn left and walk 11m (west), followed by another left turn and walk 9m south.
Distance from the tree: 13m + 9m = 22m (south)
Direction: CCW angle from east = 180°

3. Option 3: Walk 13m South, then turn left and walk 11m (west), followed by another left turn and walk 9m west.
Distance from the tree: 13m + 11m = 24m (west)
Direction: CCW angle from east = 90°

4. Option 4: Walk 13m South, then turn left and walk 11m (west), followed by another left turn and walk 9m east.
Distance from the tree: 13m - 11m = 2m (south)
Direction: CCW angle from east = 360° (equal to 0°)

So, the possible locations of the time capsule, listed in CCW order starting with the one closest to due west, are:

1. Option 3: Distance from the tree = 24m (west), Direction = 90°
2. Option 4: Distance from the tree = 2m (south), Direction = 0°
3. Option 1: Distance from the tree = 4m (south), Direction = 270°
4. Option 2: Distance from the tree = 22m (south), Direction = 180°