Let’s solve each problem step by step using the Pythagorean Theorem:
a² + b² = c², where
c is the hypotenuse (the longest side, opposite the right angle).
We’ll find the missing side for each exercise and round to the nearest tenth if needed.
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Exercise H: a = 9, b = 4, c = ?
→ c² = 9² + 4² = 81 + 16 = 97
→ c = √97 ≈ 9.8 →
✔ matches given answer
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Exercise E: a = 50, b = 50, c = ?
→ c² = 50² + 50² = 2500 + 2500 = 5000
→ c = √5000 ≈ 70.7 →
✔ matches given answer
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Now let’s do the rest:
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Exercise O: a = 8, b = 14, c = ?
→ c² = 8² + 14² = 64 + 196 = 260
→ c = √260 ≈ 16.1
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Exercise B: b = 20, c = 30, a = ?
→ a² = c² - b² = 900 - 400 = 500
→ a = √500 ≈ 22.4
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Exercise S: b = 3, c = 7, a = ?
→ a² = 7² - 3² = 49 - 9 = 40
→ a = √40 ≈ 6.3
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Exercise V: a = 6, c = 11, b = ?
→ b² = 11² - 6² = 121 - 36 = 85
→ b = √85 ≈ 9.2
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Exercise M: b = 5, c = 12, a = ?
→ a² = 12² - 5² = 144 - 25 = 119
→ a = √119 ≈ 10.9
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Exercise W: a = 1, b = 1, c = ?
→ c² = 1 + 1 = 2
→ c = √2 ≈ 1.4
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Exercise G: b = 8, c = 10, a = ?
→ a² = 100 - 64 = 36
→ a = √36 = 6.0
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Exercise X: b = 16, c = 25, a = ?
→ a² = 625 - 256 = 369
→ a = √369 ≈ 19.2
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Exercise C: a = 5, c = 6, b = ?
→ b² = 36 - 25 = 11
→ b = √11 ≈ 3.3
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Exercise A: a = 2, c = 9, b = ?
→ b² = 81 - 4 = 77
→ b = √77 ≈ 8.8
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Exercise R: a = 4, c = 15, b = ?
→ b² = 225 - 16 = 209
→ b = √209 ≈ 14.5
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Exercise L: b = 15, c = 17, a = ?
→ a² = 289 - 225 = 64
→ a = √64 = 8.0
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Exercise I: a = 12, c = 13, b = ?
→ b² = 169 - 144 = 25
→ b = √25 = 5.0
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Exercise N: a = 10, c = 22, b = ?
→ b² = 484 - 100 = 384
→ b = √384 ≈ 19.6
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Now we match each answer to its letter code from the top of the page:
From the quiz:
- 8.8 → A
- 19.6 → N
- 18.5 → ? (not used)
- 8.8 → A
- 10.9 → M
- 8.8 → A
- 3.3 → C
- 9.6 → ? (not used)
- 9.6 → ?
- 70.7 → E
- 1.4 → W
- 70.7 → E
- 14.5 → R
Wait — actually, looking at the first question: “What is the opposite of a professional eater?” — the letters above the numbers spell out words when you write the letter corresponding to each number.
But since the user just wants us to solve the math problems (and they’ve already filled in H and E), we only need to provide the missing values for the blank exercises.
So here are all the answers for the blanks:
O: c = 16.1
B: a = 22.4
S: a = 6.3
V: b = 9.2
M: a = 10.9
W: c = 1.4
G: a = 6.0
X: a = 19.2
C: b = 3.3
A: b = 8.8
R: b = 14.5
L: a = 8.0
I: b = 5.0
N: b = 19.6
All rounded to nearest tenth as instructed.
Final Answer:
O: 16.1
B: 22.4
S: 6.3
V: 9.2
M: 10.9
W: 1.4
G: 6.0
X: 19.2
C: 3.3
A: 8.8
R: 14.5
L: 8.0
I: 5.0
N: 19.6
Parent Tip: Review the logic above to help your child master the concept of cryptic quiz worksheet answers.
