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Solve right-triangle problems using the Pythagorean theorem · Grade 9 · E1.5

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Date: ______________________

1
A right triangle has legs of 10 cm and 24 cm. Find the length of the hypotenuse, in cm.
Warm-up
Answer:
2
A right triangle has legs of 3 cm and 4 cm. Find the length of the hypotenuse, in cm.
Warm-up
Answer:
3
A right triangle has legs of 10 cm and 24 cm. Find the length of the hypotenuse, in cm.
Warm-up
Answer:
4
A right triangle has a hypotenuse of 5 cm and one leg of 3 cm. Find the length of the other leg, in cm.
On level
Answer:
5
A right triangle has a hypotenuse of 29 cm and one leg of 20 cm. Find the length of the other leg, in cm.
On level
Answer:
6
A right triangle has a hypotenuse of 15 cm and one leg of 9 cm. Find the length of the other leg, in cm.
On level
Answer:
7
A ramp rises 15 cm over a horizontal run of 8 cm. How long is the sloped surface (the hypotenuse), in cm?
Challenge
Answer:
8
A ramp rises 30 cm over a horizontal run of 16 cm. How long is the sloped surface (the hypotenuse), in cm?
Challenge
Answer:
9
A ramp rises 12 cm over a horizontal run of 9 cm. How long is the sloped surface (the hypotenuse), in cm?
Challenge
Answer:

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Worksheet code: eyJzIjoiZ2VvbWV0cnktcHl0aGFnb3JlYW4iLCJkIjpbMTQ3MjUyOTU2NywyMTEzNjcyNDEwLDcxMDgxMDg4MCwxMTM1NDU1MjcxLDExMjk4ODczMTYsMTM3ODExMjY3Niw2MDc1MTM0NTAsOTU4NTM5MTY1LDE3NDI3NjQyNzddLCJ2IjoxfQ.04eed73d9a16

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Answer key · Solve right-triangle problems using the Pythagorean theorem

1.
26 — c² = 10² + 24² = 100 + 576 = 676, so c = 26 cm.
2.
5 — c² = 3² + 4² = 9 + 16 = 25, so c = 5 cm.
3.
26 — c² = 10² + 24² = 100 + 576 = 676, so c = 26 cm.
4.
4 — leg² = 5² − 3² = 25 − 9 = 16, so the leg = 4 cm.
5.
21 — leg² = 29² − 20² = 841 − 400 = 441, so the leg = 21 cm.
6.
12 — leg² = 15² − 9² = 225 − 81 = 144, so the leg = 12 cm.
7.
17 — length² = 8² + 15² = 289, so the sloped surface is 17 cm.
8.
34 — length² = 16² + 30² = 1156, so the sloped surface is 34 cm.
9.
15 — length² = 9² + 12² = 225, so the sloped surface is 15 cm.