Let’s solve each problem step by step using the Pythagorean Theorem.
The Pythagorean Theorem says:
a² + b² = c²
where
c is the hypotenuse (the longest side, opposite the right angle), and
a and
b are the other two sides.
We’ll use this formula to find missing side lengths. Remember to round to the nearest tenth if needed.
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Problem 1: Triangle with legs 5 ft and 12 ft → Find hypotenuse
Step 1: Label a = 5, b = 12, c = ?
Step 2: Plug into formula:
5² + 12² = c²
25 + 144 = c²
169 = c²
Step 3: Take square root of both sides:
c = √169 = 13
✔ Answer:
13 ft
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Problem 2: Triangle with hypotenuse 4 in, one leg 3 in → Find other leg
Step 1: Label a = ?, b = 3, c = 4
Step 2: Plug into formula:
a² + 3² = 4²
a² + 9 = 16
Step 3: Subtract 9 from both sides:
a² = 7
Step 4: Take square root:
a = √7 ≈ 2.645... → Round to nearest tenth →
2.6
✔ Answer:
2.6 in
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Problem 3: Triangle with hypotenuse 28 cm, one leg 5 cm → Find other leg
Step 1: Label a = ?, b = 5, c = 28
Step 2: Plug into formula:
a² + 5² = 28²
a² + 25 = 784
Step 3: Subtract 25 from both sides:
a² = 759
Step 4: Take square root:
a = √759 ≈ 27.55... → Round to nearest tenth →
27.6
✔ Answer:
27.6 cm
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Problem 4: Triangle with hypotenuse 21 ft, one leg 15 ft → Find other leg
Step 1: Label a = ?, b = 15, c = 21
Step 2: Plug into formula:
a² + 15² = 21²
a² + 225 = 441
Step 3: Subtract 225 from both sides:
a² = 216
Step 4: Take square root:
a = √216 ≈ 14.696... → Round to nearest tenth →
14.7
✔ Answer:
14.7 ft
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Final Answer:
Problem 1: 13 ft
Problem 2: 2.6 in
Problem 3: 27.6 cm
Problem 4: 14.7 ft
Parent Tip: Review the logic above to help your child master the concept of the pythagorean theorem worksheet answer key.
