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Grade 10 Special Right Triangles Worksheet with Answers

Grade 10 (US) · Year 11 (UK) · Class 10 (India) · Math

Unit 3: TrianglesRight TrianglesCCSS G-SRT.C.6

Exact side lengths in 45-45-90 and 30-60-90 triangles. This free high 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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Special Right Triangles

Grade 10 · Math

Score___ / 12

Name

Class

Date

Learning goal: Right Triangles · CCSS G-SRT.C.6

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

Example

In a 30-60-90 triangle the shorter leg is 7. Find the longer leg and the hypotenuse.

Answer: longer leg 7√3, hypotenuse 14

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 45-45-90 triangle has a hypotenuse of 2√2. How long is each leg?

    Answer
  2. 2

    In a 30-60-90 triangle the hypotenuse is 8. Find the shorter leg and the longer leg.

    Show your work
    Answer
  3. 3

    A 45-45-90 triangle has legs of length 3. How long is the hypotenuse?

    33?
    Answer
  4. 4

    In a 30-60-90 triangle the shorter leg is 3. Find the longer leg and the hypotenuse.

    ?3?
    Answer
  5. 5

    In a 30-60-90 triangle the shorter leg is 9. Find the longer leg and the hypotenuse.

    ?9?
    Answer
  6. 6

    A 45-45-90 triangle has legs of length 4. How long is the hypotenuse?

    44?
    Answer
  7. 7

    A 45-45-90 triangle has legs of length 6. How long is the hypotenuse?

    66?
    Answer
  8. 8

    A 45-45-90 triangle has a hypotenuse of 6√2. How long is each leg?

    Answer
  9. 9

    In a 30-60-90 triangle the shorter leg is 10. Find the longer leg and the hypotenuse.

    ?10?
    Answer
  10. 10

    In a 30-60-90 triangle the shorter leg is 4. Find the longer leg and the hypotenuse.

    ?4?
    Answer
  11. 11

    A 45-45-90 triangle has a hypotenuse of 7√2. How long is each leg?

    Answer
  12. 12

    A 45-45-90 triangle has legs of length 7. How long is the hypotenuse?

    77?
    Answer

★ Challenge corner for fast finishers

You have 6 shirts, 2 pairs of pants and 2 hats. How many different outfits of one shirt, one pair of pants and one hat can you make?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/10/special_right_triangles

Answer key (click to show)
  1. 1.2
  2. 2.shorter leg 4, longer leg 4√3
  3. 3.3√2
  4. 4.longer leg 3√3, hypotenuse 6
  5. 5.longer leg 9√3, hypotenuse 18
  6. 6.4√2
  7. 7.6√2
  8. 8.6
  9. 9.longer leg 10√3, hypotenuse 20
  10. 10.longer leg 4√3, hypotenuse 8
  11. 11.7
  12. 12.7√2
  13. ★24 (challenge corner)

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