Or press and hold the picture and choose “Save image”.
for Whoobee's shop
Pythagorean Theorem: Missing Legs & Word Problems — Easy Worksheet 1
Grade 8 · MathSheets Name: ____________________ Date: __________
Use a^2 + b^2 = c^2. Round to the nearest tenth when the answer is not a whole number.
How to solve
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Example
A right triangle has a leg of 10 and a hypotenuse of 26. Find the other leg.
Answer: 24
Not quite. The answer is
💡 Use a2 + b2 = c2 with the hypotenuse c = 17. b2 = 172 − 152 = 289 − 225 = 64, so b = √64 = 8. The other leg is 8.
✓ Correct!
Not quite. The answer is
💡 Use a2 + b2 = c2 with the hypotenuse c = 17. b2 = 172 − 152 = 289 − 225 = 64, so b = √64 = 8. The other leg is 8.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A right triangle has a leg of 5 and a hypotenuse of 13. Find the other leg.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The wall, the ground and the ladder make a right triangle, and the ladder is the hypotenuse. b2 = 172 − 82 = 289 − 64 = 225, so b = √225 = 15. The ladder reaches 15 feet up the wall.
✓ Correct!
Not quite. The answer is
💡 The wall, the ground and the ladder make a right triangle, and the ladder is the hypotenuse. b2 = 172 − 82 = 289 − 64 = 225, so b = √225 = 15. The ladder reaches 15 feet up the wall.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A right triangle has a leg of 6 and a hypotenuse of 10. Find the other leg.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use a2 + b2 = c2 with the hypotenuse c = 20. b2 = 202 − 162 = 400 − 256 = 144, so b = √144 = 12. The other leg is 12.
✓ Correct!
Not quite. The answer is
💡 Use a2 + b2 = c2 with the hypotenuse c = 20. b2 = 202 − 162 = 400 − 256 = 144, so b = √144 = 12. The other leg is 12.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A right triangle has a leg of 21 and a hypotenuse of 29. Find the other leg.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The width, the height and the diagonal make a right triangle, and the diagonal is the hypotenuse. c2 = 82 + 152 = 64 + 225 = 289, so c = √289 = 17. The diagonal is 17 inches long.
✓ Correct!
Not quite. The answer is
💡 The width, the height and the diagonal make a right triangle, and the diagonal is the hypotenuse. c2 = 82 + 152 = 64 + 225 = 289, so c = √289 = 17. The diagonal is 17 inches long.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A right triangle has a leg of 10 and a hypotenuse of 26. Find the other leg.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use a2 + b2 = c2 with the hypotenuse c = 5. b2 = 52 − 32 = 25 − 9 = 16, so b = √16 = 4. The other leg is 4.
✓ Correct!
Not quite. The answer is
💡 Use a2 + b2 = c2 with the hypotenuse c = 5. b2 = 52 − 32 = 25 − 9 = 16, so b = √16 = 4. The other leg is 4.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A right triangle has a leg of 9 and a hypotenuse of 15. Find the other leg.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The wall, the ground and the ladder make a right triangle, and the ladder is the hypotenuse. b2 = 202 − 162 = 400 − 256 = 144, so b = √144 = 12. The ladder reaches 12 feet up the wall.
✓ Correct!
Not quite. The answer is
💡 The wall, the ground and the ladder make a right triangle, and the ladder is the hypotenuse. b2 = 202 − 162 = 400 − 256 = 144, so b = √144 = 12. The ladder reaches 12 feet up the wall.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A right triangle has a leg of 24 and a hypotenuse of 26. Find the other leg.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Use a2 + b2 = c2 with the hypotenuse c = 10. b2 = 102 − 62 = 100 − 36 = 64, so b = √64 = 8. The other leg is 8.
✓ Correct!
Not quite. The answer is
💡 Use a2 + b2 = c2 with the hypotenuse c = 10. b2 = 102 − 62 = 100 − 36 = 64, so b = √64 = 8. The other leg is 8.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A 5-foot ladder leans against a wall. Its foot is 3 feet from the wall. How high up the wall does the ladder reach?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The width, the height and the diagonal make a right triangle, and the diagonal is the hypotenuse. c2 = 102 + 242 = 100 + 576 = 676, so c = √676 = 26. The diagonal is 26 inches long.
✓ Correct!
Not quite. The answer is
💡 The width, the height and the diagonal make a right triangle, and the diagonal is the hypotenuse. c2 = 102 + 242 = 100 + 576 = 676, so c = √676 = 26. The diagonal is 26 inches long.
💡 How to solve: Pythagorean Theorem: Missing Legs & Word Problems
In a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. To find a missing leg, subtract: b2 = c2 - a2, then take the square root. For the diagonal of a box, first find the diagonal of the base, then use it as a leg with the height: d2 = l2 + w2 + h2.
Try a similar one
A right triangle has a leg of 3 and a hypotenuse of 5. Find the other leg.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Log in to save your progress.
Pythagorean Theorem: Missing Legs & Word Problems — Easy Worksheet 1
Use a^2 + b^2 = c^2. Round to the nearest tenth when the answer is not a whole number.