GCSE Maths Revision: Pythagoras Theorem Worksheet. | Teaching ... - Free Printable

I will solve the problem by calculating the missing side lengths for each of the nine right-angled triangles using the Pythagorean theorem, which states that for any right-angled triangle, $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the two shorter sides (legs), and $c$ is the length of the hypotenuse.

I will go through each problem one by one.

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Problem 1:
- Given: $a = 8$ cm, $b = 15$ cm
- Find: $c$
- Calculation: $c^2 = 8^2 + 15^2 = 64 + 225 = 289$
- Therefore, $c = \sqrt{289} = 17$ cm

Problem 2:
- Given: $a = 16$ cm, $b = 30$ cm
- Find: $c$
- Calculation: $c^2 = 16^2 + 30^2 = 256 + 900 = 1156$
- Therefore, $c = \sqrt{1156} = 34$ cm

Problem 3:
- Given: $a = 40$ cm, $b = 75$ cm
- Find: $c$
- Calculation: $c^2 = 40^2 + 75^2 = 1600 + 5625 = 7225$
- Therefore, $c = \sqrt{7225} = 85$ cm

Problem 4:
- Given: $a = 15$ cm, $c = 25$ cm
- Find: $b$
- Calculation: $b^2 = c^2 - a^2 = 25^2 - 15^2 = 625 - 225 = 400$
- Therefore, $b = \sqrt{400} = 20$ cm

Problem 5:
- Given: $a = 18$ cm, $c = 30$ cm
- Find: $b$
- Calculation: $b^2 = c^2 - a^2 = 30^2 - 18^2 = 900 - 324 = 576$
- Therefore, $b = \sqrt{576} = 24$ cm

Problem 6:
- Given: $a = 20$ cm, $c = 52$ cm
- Find: $b$
- Calculation: $b^2 = c^2 - a^2 = 52^2 - 20^2 = 2704 - 400 = 2304$
- Therefore, $b = \sqrt{2304} = 48$ cm

Problem 7:
- Given: $b = 48$ cm, $c = 60$ cm
- Find: $a$
- Calculation: $a^2 = c^2 - b^2 = 60^2 - 48^2 = 3600 - 2304 = 1296$
- Therefore, $a = \sqrt{1296} = 36$ cm

Problem 8:
- Given: $b = 28$ cm, $c = 35$ cm
- Find: $a$
- Calculation: $a^2 = c^2 - b^2 = 35^2 - 28^2 = 1225 - 784 = 441$
- Therefore, $a = \sqrt{441} = 21$ cm

Problem 9:
- Given: $b = 60$ cm, $c = 68$ cm
- Find: $a$
- Calculation: $a^2 = c^2 - b^2 = 68^2 - 60^2 = 4624 - 3600 = 1024$
- Therefore, $a = \sqrt{1024} = 32$ cm

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Final Answers:

1. c = 17 cm
2. c = 34 cm
3. c = 85 cm
4. b = 20 cm
5. b = 24 cm
6. b = 48 cm
7. a = 36 cm
8. a = 21 cm
9. a = 32 cm