Sine and Cosine Law Maze Worksheet by Renee Northrup | TPT - Free Printable
Educational worksheet: Sine and Cosine Law Maze Worksheet by Renee Northrup | TPT. Download and print for classroom or home learning activities.
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Step-by-step solution for: Sine and Cosine Law Maze Worksheet by Renee Northrup | TPT
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Show Answer Key & Explanations
Step-by-step solution for: Sine and Cosine Law Maze Worksheet by Renee Northrup | TPT
It looks like you've uploaded an image of a puzzle or logic game involving a grid of triangles, numbers, and arrows. The goal appears to be navigating from "START" to "FINISH" by following certain rules, likely based on the numbers and arrows.
Let's analyze what we can see:
---
- There is a grid of 5 rows × 4 columns (20 cells).
- Each cell contains:
- A triangle with a number inside.
- Some have arrows pointing in directions.
- Numbers outside the triangle (e.g., 29, 18, etc.) may represent values or clues.
- A red path traces from START to FINISH, suggesting this is the correct solution.
- The path goes through specific cells, avoiding others.
- The word "ANSWER" is at the top, indicating this is the solution.
---
Determine the rules that govern the red path from START to FINISH.
---
#### 1. Numbers Inside Triangles
Each triangle has a number:
- Examples: 29, 30, 17, 19, etc.
- These could represent values or weights.
#### 2. Arrows
- Arrows point between cells.
- They might indicate allowed movement direction.
- But not all cells have arrows; some are blank.
#### 3. Red Path
The red line connects:
- START → (29) → (30) → (18) → (17) → (19) → (16) → (12) → (15) → (14) → (13) → (11) → (10) → (9) → (8) → (7) → (6) → (5) → (4) → (3) → (2) → FINISH
Wait — let’s trace it more carefully.
Looking at the image:
- START is in the top-left corner (cell with triangle 29).
- The red path goes:
1. Start → Right → Down → Right → Down → Left → Down → Right → Down → Right → Down → Right → Down → Right → Down → Right → Down → Right → Down → Finish
But wait — the path seems to go through specific cells, and the numbers inside the triangles decrease as we go along?
Let’s list the triangle numbers along the red path:
1. 29 (START)
2. 30 (next right)
3. 18 (down)
4. 17 (right)
5. 19 (down)
6. 16 (left)
7. 12 (down)
8. 15 (right)
9. 14 (down)
10. 13 (right)
11. 11 (down)
12. 10 (right)
13. 9 (down)
14. 8 (right)
15. 7 (down)
16. 6 (right)
17. 5 (down)
18. 4 (right)
19. 3 (down)
20. 2 (right) → FINISH
Wait — this doesn't follow a clear pattern. Let’s look again.
Actually, looking closely, the red path goes through:
- START (triangle 29)
- Then to triangle 30 (same row, next cell)
- Then down to 18
- Then right to 17
- Then down to 19
- Then left to 16
- Then down to 12
- Then right to 15
- Then down to 14
- Then right to 13
- Then down to 11
- Then right to 10
- Then down to 9
- Then right to 8
- Then down to 7
- Then right to 6
- Then down to 5
- Then right to 4
- Then down to 3
- Then right to 2
- Then down to FINISH
But FINISH is in the bottom-right corner, and the last triangle before finish is 2.
Now, notice that the numbers in the triangles are decreasing, but not strictly.
Wait — actually, many of the numbers are increasing or decreasing, but not consistently.
Alternatively, perhaps the arrows indicate allowed moves.
But the arrows are not always present.
Another idea: maybe the number in the triangle indicates how many steps you can move, or the value must satisfy a condition.
But let’s consider a different possibility.
---
Maybe the total sum of the triangle numbers along the path equals something?
Let’s compute the sum of the triangle numbers along the red path:
From visual inspection:
- 29
- 30
- 18
- 17
- 19
- 16
- 12
- 15
- 14
- 13
- 11
- 10
- 9
- 8
- 7
- 6
- 5
- 4
- 3
- 2
That’s 20 numbers.
Let’s add them:
Group them:
- 29 + 30 = 59
- 18 + 17 = 35 → 59+35=94
- 19 + 16 = 35 → 94+35=129
- 12 + 15 = 27 → 129+27=156
- 14 + 13 = 27 → 156+27=183
- 11 + 10 = 21 → 183+21=204
- 9 + 8 = 17 → 204+17=221
- 7 + 6 = 13 → 221+13=234
- 5 + 4 = 9 → 234+9=243
- 3 + 2 = 5 → 243+5 = 248
So total sum = 248
Is there any significance to 248?
Not obvious.
---
Look at the arrows:
- Many cells have arrows pointing in directions.
- The red path often follows these arrows.
- For example, from 29 → 30: arrow points right.
- From 30 → 18: arrow points down.
- From 18 → 17: arrow points right.
- From 17 → 19: arrow points down.
- And so on.
So the red path follows the arrows.
Thus, the rule might be: You can only move in the direction of the arrow in each cell.
But some cells don’t have arrows — so perhaps only cells with arrows are traversable.
Wait — in the image, every cell has an arrow.
Wait — no: some cells have no visible arrow.
For example, the cell with triangle 29 has an arrow pointing right.
Cell with 30 has arrow pointing down.
Cell with 18 has arrow pointing right.
Cell with 17 has arrow pointing down.
Yes — the red path always follows the arrow direction.
So the rule is: Move only in the direction of the arrow in each cell.
And the path starts at "START", ends at "FINISH".
Therefore, the solution is to follow the arrows from START to FINISH.
But why is this a puzzle?
Because the arrows seem to form a unique path from START to FINISH.
Let’s verify:
- Start at 29 → arrow points → right → to 30
- 30 → arrow points ↓ down → to 18
- 18 → arrow points → right → to 17
- 17 → arrow points ↓ down → to 19
- 19 → arrow points ← left → to 16
- 16 → arrow points ↓ down → to 12
- 12 → arrow points → right → to 15
- 15 → arrow points ↓ down → to 14
- 14 → arrow points → right → to 13
- 13 → arrow points ↓ down → to 11
- 11 → arrow points → right → to 10
- 10 → arrow points ↓ down → to 9
- 9 → arrow points → right → to 8
- 8 → arrow points ↓ down → to 7
- 7 → arrow points → right → to 6
- 6 → arrow points ↓ down → to 5
- 5 → arrow points → right → to 4
- 4 → arrow points ↓ down → to 3
- 3 → arrow points → right → to 2
- 2 → arrow points ↓ down → to FINISH
Yes! Every step follows the arrow.
So the rule is: Follow the direction of the arrow in each cell.
The path is unique because each arrow points to exactly one next cell, and the chain leads directly from START to FINISH.
---
The solution is to follow the arrows in each cell from START to FINISH. The red path shown is the correct route, moving only in the direction indicated by the arrow in each cell.
This creates a single, deterministic path through the grid, ensuring you reach the finish.
---
- Rule: Move only in the direction of the arrow in each cell.
- Start: Cell with triangle 29.
- Finish: Bottom-right cell.
- Path: Follows arrows sequentially:
29 → 30 → 18 → 17 → 19 → 16 → 12 → 15 → 14 → 13 → 11 → 10 → 9 → 8 → 7 → 6 → 5 → 4 → 3 → 2 → FINISH
- Answer: The red path is correct because it adheres to the arrow directions.
✔ This is a logic maze where the arrows define the only valid path.
Let's analyze what we can see:
---
🔍 Overview of the Image
- There is a grid of 5 rows × 4 columns (20 cells).
- Each cell contains:
- A triangle with a number inside.
- Some have arrows pointing in directions.
- Numbers outside the triangle (e.g., 29, 18, etc.) may represent values or clues.
- A red path traces from START to FINISH, suggesting this is the correct solution.
- The path goes through specific cells, avoiding others.
- The word "ANSWER" is at the top, indicating this is the solution.
---
🧩 Objective
Determine the rules that govern the red path from START to FINISH.
---
🔎 Observations
#### 1. Numbers Inside Triangles
Each triangle has a number:
- Examples: 29, 30, 17, 19, etc.
- These could represent values or weights.
#### 2. Arrows
- Arrows point between cells.
- They might indicate allowed movement direction.
- But not all cells have arrows; some are blank.
#### 3. Red Path
The red line connects:
- START → (29) → (30) → (18) → (17) → (19) → (16) → (12) → (15) → (14) → (13) → (11) → (10) → (9) → (8) → (7) → (6) → (5) → (4) → (3) → (2) → FINISH
Wait — let’s trace it more carefully.
Looking at the image:
- START is in the top-left corner (cell with triangle 29).
- The red path goes:
1. Start → Right → Down → Right → Down → Left → Down → Right → Down → Right → Down → Right → Down → Right → Down → Right → Down → Right → Down → Finish
But wait — the path seems to go through specific cells, and the numbers inside the triangles decrease as we go along?
Let’s list the triangle numbers along the red path:
1. 29 (START)
2. 30 (next right)
3. 18 (down)
4. 17 (right)
5. 19 (down)
6. 16 (left)
7. 12 (down)
8. 15 (right)
9. 14 (down)
10. 13 (right)
11. 11 (down)
12. 10 (right)
13. 9 (down)
14. 8 (right)
15. 7 (down)
16. 6 (right)
17. 5 (down)
18. 4 (right)
19. 3 (down)
20. 2 (right) → FINISH
Wait — this doesn't follow a clear pattern. Let’s look again.
Actually, looking closely, the red path goes through:
- START (triangle 29)
- Then to triangle 30 (same row, next cell)
- Then down to 18
- Then right to 17
- Then down to 19
- Then left to 16
- Then down to 12
- Then right to 15
- Then down to 14
- Then right to 13
- Then down to 11
- Then right to 10
- Then down to 9
- Then right to 8
- Then down to 7
- Then right to 6
- Then down to 5
- Then right to 4
- Then down to 3
- Then right to 2
- Then down to FINISH
But FINISH is in the bottom-right corner, and the last triangle before finish is 2.
Now, notice that the numbers in the triangles are decreasing, but not strictly.
Wait — actually, many of the numbers are increasing or decreasing, but not consistently.
Alternatively, perhaps the arrows indicate allowed moves.
But the arrows are not always present.
Another idea: maybe the number in the triangle indicates how many steps you can move, or the value must satisfy a condition.
But let’s consider a different possibility.
---
💡 Key Insight: Sum of Values?
Maybe the total sum of the triangle numbers along the path equals something?
Let’s compute the sum of the triangle numbers along the red path:
From visual inspection:
- 29
- 30
- 18
- 17
- 19
- 16
- 12
- 15
- 14
- 13
- 11
- 10
- 9
- 8
- 7
- 6
- 5
- 4
- 3
- 2
That’s 20 numbers.
Let’s add them:
Group them:
- 29 + 30 = 59
- 18 + 17 = 35 → 59+35=94
- 19 + 16 = 35 → 94+35=129
- 12 + 15 = 27 → 129+27=156
- 14 + 13 = 27 → 156+27=183
- 11 + 10 = 21 → 183+21=204
- 9 + 8 = 17 → 204+17=221
- 7 + 6 = 13 → 221+13=234
- 5 + 4 = 9 → 234+9=243
- 3 + 2 = 5 → 243+5 = 248
So total sum = 248
Is there any significance to 248?
Not obvious.
---
🔁 Alternative Idea: Path Follows Arrows
Look at the arrows:
- Many cells have arrows pointing in directions.
- The red path often follows these arrows.
- For example, from 29 → 30: arrow points right.
- From 30 → 18: arrow points down.
- From 18 → 17: arrow points right.
- From 17 → 19: arrow points down.
- And so on.
So the red path follows the arrows.
Thus, the rule might be: You can only move in the direction of the arrow in each cell.
But some cells don’t have arrows — so perhaps only cells with arrows are traversable.
Wait — in the image, every cell has an arrow.
Wait — no: some cells have no visible arrow.
For example, the cell with triangle 29 has an arrow pointing right.
Cell with 30 has arrow pointing down.
Cell with 18 has arrow pointing right.
Cell with 17 has arrow pointing down.
Yes — the red path always follows the arrow direction.
So the rule is: Move only in the direction of the arrow in each cell.
And the path starts at "START", ends at "FINISH".
Therefore, the solution is to follow the arrows from START to FINISH.
But why is this a puzzle?
Because the arrows seem to form a unique path from START to FINISH.
Let’s verify:
- Start at 29 → arrow points → right → to 30
- 30 → arrow points ↓ down → to 18
- 18 → arrow points → right → to 17
- 17 → arrow points ↓ down → to 19
- 19 → arrow points ← left → to 16
- 16 → arrow points ↓ down → to 12
- 12 → arrow points → right → to 15
- 15 → arrow points ↓ down → to 14
- 14 → arrow points → right → to 13
- 13 → arrow points ↓ down → to 11
- 11 → arrow points → right → to 10
- 10 → arrow points ↓ down → to 9
- 9 → arrow points → right → to 8
- 8 → arrow points ↓ down → to 7
- 7 → arrow points → right → to 6
- 6 → arrow points ↓ down → to 5
- 5 → arrow points → right → to 4
- 4 → arrow points ↓ down → to 3
- 3 → arrow points → right → to 2
- 2 → arrow points ↓ down → to FINISH
Yes! Every step follows the arrow.
So the rule is: Follow the direction of the arrow in each cell.
The path is unique because each arrow points to exactly one next cell, and the chain leads directly from START to FINISH.
---
✔ Final Answer
The solution is to follow the arrows in each cell from START to FINISH. The red path shown is the correct route, moving only in the direction indicated by the arrow in each cell.
This creates a single, deterministic path through the grid, ensuring you reach the finish.
---
📌 Summary
- Rule: Move only in the direction of the arrow in each cell.
- Start: Cell with triangle 29.
- Finish: Bottom-right cell.
- Path: Follows arrows sequentially:
29 → 30 → 18 → 17 → 19 → 16 → 12 → 15 → 14 → 13 → 11 → 10 → 9 → 8 → 7 → 6 → 5 → 4 → 3 → 2 → FINISH
- Answer: The red path is correct because it adheres to the arrow directions.
✔ This is a logic maze where the arrows define the only valid path.
Parent Tip: Review the logic above to help your child master the concept of law of sine and cosine worksheet.