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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 3 cm and 4 cm. Find the length of the hypotenuse, in cm.
Warm-up
Answer:
2
A right triangle has legs of 7 cm and 24 cm. Find the length of the hypotenuse, in cm.
Warm-up
Answer:
3
A right triangle has legs of 8 cm and 15 cm. Find the length of the hypotenuse, in cm.
Warm-up
Answer:
4
A right triangle has a hypotenuse of 26 cm and one leg of 10 cm. Find the length of the other leg, in cm.
On level
Answer:
5
A right triangle has a hypotenuse of 25 cm and one leg of 7 cm. Find the length of the other leg, in cm.
On level
Answer:
6
A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. Find the length of the other leg, in cm.
On level
Answer:
7
A ramp rises 60 cm over a horizontal run of 32 cm. How long is the sloped surface (the hypotenuse), in cm?
Challenge
Answer:
8
A ramp rises 12 cm over a horizontal run of 5 cm. How long is the sloped surface (the hypotenuse), in cm?
Challenge
Answer:
9
A ramp rises 12 cm over a horizontal run of 5 cm. How long is the sloped surface (the hypotenuse), in cm?
Challenge
Answer:

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Worksheet code: eyJzIjoiZ2VvbWV0cnktcHl0aGFnb3JlYW4iLCJkIjpbODA4MDQzMzA1LDEzNDU2OTE1NjUsODk5Mjk1MTQ2LDE1MzY5NDk4ODMsMjEwOTI3MzAxLDU2OTQwNTQyMSwxMTY2NTQ3NjY1LDYxMjk0MDE2MSwxNDQzNzIxNTgxXSwidiI6MX0.175f897bc773

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

1.
5 — c² = 3² + 4² = 9 + 16 = 25, so c = 5 cm.
2.
25 — c² = 7² + 24² = 49 + 576 = 625, so c = 25 cm.
3.
17 — c² = 8² + 15² = 64 + 225 = 289, so c = 17 cm.
4.
24 — leg² = 26² − 10² = 676 − 100 = 576, so the leg = 24 cm.
5.
24 — leg² = 25² − 7² = 625 − 49 = 576, so the leg = 24 cm.
6.
8 — leg² = 10² − 6² = 100 − 36 = 64, so the leg = 8 cm.
7.
68 — length² = 32² + 60² = 4624, so the sloped surface is 68 cm.
8.
13 — length² = 5² + 12² = 169, so the sloped surface is 13 cm.
9.
13 — length² = 5² + 12² = 169, so the sloped surface is 13 cm.