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Grade 7 Pythagorean Theorem Worksheet with Answers

Grade 7 (US) · Year 8 (UK) · Class 7 (India) · Math

Unit 7: Going FurtherAdvanced: Grade 8 PreviewCCSS 8.G.B.7Advanced

Finding a missing side of a right triangle with a² + b² = c². This free middle school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Pythagorean Theorem

Grade 7 · Math

Score___ / 12

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Class

Date

Learning goal: Advanced: Grade 8 Preview · CCSS 8.G.B.7

Directions: Use the pictures to help you. Solve each problem. Show your work, then write your answer in the box.

Example

A right triangle has legs of 3 m and 4 m. Find the hypotenuse.

Answer: 5 m

RememberRight triangles

θa (adjacent)b (opposite)c (hypotenuse)a² + b² = c²c is the longest side,opposite the right angle.sin θ = opp ÷ hyp (SOH)cos θ = adj ÷ hyp (CAH)tan θ = opp ÷ adj (TOA)
  1. 1

    A 5 ft ladder leans against a wall with its foot 3 ft from the wall. How high up the wall does it reach?

    3 ft?5 ft
    Answer
  2. 2

    A right triangle has a hypotenuse of 17 m and one leg of 8 m. Find the other leg.

    8 m?17 m
    Answer
  3. 3

    A 10 cm ladder leans against a wall with its foot 6 cm from the wall. How high up the wall does it reach?

    6 cm?10 cm
    Answer
  4. 4

    A right triangle has legs of 7 m and 24 m. Find the hypotenuse.

    24 m7 m?
    Answer
  5. 5

    A right triangle has legs of 14 ft and 48 ft. Find the hypotenuse.

    48 ft14 ft?
    Answer
  6. 6

    A right triangle has legs of 20 cm and 21 cm. Find the hypotenuse.

    21 cm20 cm?
    Answer
  7. 7

    A right triangle has legs of 9 cm and 40 cm. Find the hypotenuse.

    40 cm9 cm?
    Answer
  8. 8

    A 41 cm ladder leans against a wall with its foot 9 cm from the wall. How high up the wall does it reach?

    9 cm?41 cm
    Answer
  9. 9

    A 41 m ladder leans against a wall with its foot 9 m from the wall. How high up the wall does it reach?

    9 m?41 m
    Answer
  10. 10

    A right triangle has legs of 16 ft and 30 ft. Find the hypotenuse.

    30 ft16 ft?
    Answer
  11. 11

    A 15 in ladder leans against a wall with its foot 9 in from the wall. How high up the wall does it reach?

    9 in?15 in
    Answer
  12. 12

    A right triangle has legs of 15 m and 36 m. Find the hypotenuse.

    36 m15 m?
    Answer

★ Challenge corner for fast finishers

How many factors does 90 have?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/7/pythagorean

Answer key (click to show)
  1. 1.4 ft
  2. 2.15 m
  3. 3.8 cm
  4. 4.25 m
  5. 5.50 ft
  6. 6.29 cm
  7. 7.41 cm
  8. 8.40 cm
  9. 9.40 m
  10. 10.34 ft
  11. 11.12 in
  12. 12.39 m
  13. ★12 (challenge corner)

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