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🎓 Grades 7-9📄 Free PDF✅ Answer Keys♾️ Unlimited Generator

Finding a Missing Leg )FREEWorksheet Generator(Grades 7-9)

Generate free printable finding missing leg worksheets with right triangle diagrams and step-by-step solutions. Practice rearranging a² = c² - b² for Grades 7–9.

📐Aligned to Common Core State Standards (CCSS)·15-20 min per sheet
🎯 Pythagorean Theorem Worksheets:Switch to Squares, Cubes & Radicals (x² & √x) ➔
Pythagorean TriplesFind Hypotenuse cFind Missing Lega = √(c²-b²)Master Generator
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📄 Sheet #1•8 Problems
PanMaths.comFinding a Missing Leg Worksheet Generator with Answers (a = √(c² - b²)) • Worksheet #1
Name: __________________________
Date: _____________ Period: ____
Score: _____ / 8
1.FIND LEG B
a = 8b = ?c = 17
b =
2.FIND LEG B
a = 15b = ?c = 25
b =
3.FIND LEG A
a = ?b = 20c = 25
a =
4.FIND LEG A
a = ?b = 8c = 10
a =
5.FIND LEG B
a = 10b = ?c = 26
b =
6.FIND LEG B
a = 9b = ?c = 15
b =
7.FIND LEG B
a = 9b = ?c = 41
b =
8.FIND LEG A
a = ?b = 16c = 20
a =
PanMaths.com • Free Math Worksheet GeneratorPage 1 of 2
PanMaths.comAnswer Key & Worked Solutions • Worksheet #1
Answer Key
Total Problems: 8
1.FIND LEG B
a = 8b = ?c = 17
b =15
1. Pythagorean Theorem: a² + b² = c² (for right triangles)
2. Rearrange for Leg b: b² = c² − a²
3. Substitute Values: b² = 17² − 8² = 289 − 64 = 225
2.FIND LEG B
a = 15b = ?c = 25
b =20
1. Pythagorean Theorem: a² + b² = c² (for right triangles)
2. Rearrange for Leg b: b² = c² − a²
3. Substitute Values: b² = 25² − 15² = 625 − 225 = 400
3.FIND LEG A
a = ?b = 20c = 25
a =15
1. Pythagorean Theorem: a² + b² = c² (for right triangles)
2. Rearrange for Leg a: a² = c² − b²
3. Substitute Values: a² = 25² − 20² = 625 − 400 = 225
4.FIND LEG A
a = ?b = 8c = 10
a =6
1. Pythagorean Theorem: a² + b² = c² (for right triangles)
2. Rearrange for Leg a: a² = c² − b²
3. Substitute Values: a² = 10² − 8² = 100 − 64 = 36
5.FIND LEG B
a = 10b = ?c = 26
b =24
1. Pythagorean Theorem: a² + b² = c² (for right triangles)
2. Rearrange for Leg b: b² = c² − a²
3. Substitute Values: b² = 26² − 10² = 676 − 100 = 576
6.FIND LEG B
a = 9b = ?c = 15
b =12
1. Pythagorean Theorem: a² + b² = c² (for right triangles)
2. Rearrange for Leg b: b² = c² − a²
3. Substitute Values: b² = 15² − 9² = 225 − 81 = 144
7.FIND LEG B
a = 9b = ?c = 41
b =40
1. Pythagorean Theorem: a² + b² = c² (for right triangles)
2. Rearrange for Leg b: b² = c² − a²
3. Substitute Values: b² = 41² − 9² = 1681 − 81 = 1600
8.FIND LEG A
a = ?b = 16c = 20
a =12
1. Pythagorean Theorem: a² + b² = c² (for right triangles)
2. Rearrange for Leg a: a² = c² − b²
3. Substitute Values: a² = 20² − 16² = 400 − 256 = 144
PanMaths.com • Answer Key & Worked SolutionsPage 2 of 2
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Worksheet Info

Categorygeometry
Grade LevelGrades 7-9 (Pre-Algebra & Geometry)
DifficultyIntermediate (Rearranging Pythagorean Theorem to solve for unknown leg a or b)
Time15-20 min

Skills Practiced

  • ✓ Rearranging the Pythagorean Theorem: leg² = c² − otherLeg²
  • ✓ Subtracting squares accurately: c² − b² (avoiding the addition trap)
  • ✓ Evaluating principal square roots of differences
  • ✓ Differentiating between hypotenuse (c) and perpendicular legs (a, b)
  • ✓ Reading right triangle diagrams with labeled unknown legs

Related Worksheets

The Step-by-Step Subtraction Protocol for Missing Legs

When solving for a missing leg, train students to execute this consistent 4-step sequence:

  1. Step 1 (Identify Sides): Label the known hypotenuse as c and the known leg as b (or a).
  2. Step 2 (Set Up Subtraction): Write the rearranged formula: a² = c² − b².
  3. Step 3 (Square & Subtract): Calculate the squares and find their difference (e.g. if c = 13 and b = 12, then a² = 13² − 12² = 169 − 144 = 25).
  4. Step 4 (Take Square Root): Evaluate the square root: a = √25 = 5.

The Addition Trap: Why Context Matters

When students learn the Pythagorean Theorem as simply "a² + b² = c²", their instinct is to square whatever two numbers they see on the paper and add them. If given c = 10 and b = 6, adding gives 100 + 36 = 136 ➔ √136 ≈ 11.66, which is completely incorrect because a leg cannot be longer than the hypotenuse 10!

Highlighting the unknown side in red on our visual diagrams trains students to inspect the triangle structure before choosing whether to add (finding c) or subtract (finding a or b).

Anti-Cheat Classroom Versions & Step-by-Step Answer Keys

Educators can print Set A and Set B shuffled sets with 6, 8, 10, 12, or 15 problems per sheet. Every problem includes a vector diagram, right angle box, and side callouts. The answer key displays the full algebraic rearrangement line, the difference of squares, and the exact integer leg length.