Pythagorean Theorem Worksheet
Goal: Use the Pythagorean theorem to find the hypotenuse or a missing leg of a right triangle, and apply it to a real-world problem.
What to do
- Open the Pythagorean calculator and keep “Find the hypotenuse” selected.
- For each of the first four rows, enter the legs in “Known leg a” and “Known leg b / hypotenuse c”. Record leg b, the hypotenuse, the area and angle A.
- Press “Find a missing leg”. The second box now holds the hypotenuse. Fill in the last two rows the same way, recording the missing leg b.
Record your results
| Setting | Leg b | Hypotenuse c | Area | Angle A |
|---|---|---|---|---|
| Legs 3 and 4 | ||||
| Legs 6 and 8 | ||||
| Legs 5 and 12 | ||||
| Legs 1 and 1 | ||||
| Leg 9, hypotenuse 15 | ||||
| Leg 5, hypotenuse 13 |
Questions
Check the 5–12 triangle by hand with a² + b² = c².
Compare the 3–4–5 and 6–8–10 triangles. What stays the same, and what changes?
The legs 1 and 1 give a hypotenuse of about 1.414. What is its exact value?
A 13-foot ladder leans against a wall with its foot 5 feet from the wall. How high up the wall does it reach?
Find the missing leg when a = 9 and c = 15. Which famous triangle is this a multiple of?
Can a leg ever be longer than the hypotenuse? Try a = 20 and c = 15 in missing-leg mode, and explain the message.
Free from Geometry Lab · geometrylab.net · 8.G.B.7: Apply the Pythagorean theorem to find unknown side lengths in right triangles in real-world and mathematical problems. HSG-SRT.C.8: Use trigonometric ratios and the Pythagorean theorem to solve right triangles in applied problems.
Teaching with this? Find the answer key and more activities on the Geometry Lab for teachers page.