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Grade 10 Law of Sines & Law of Cosines Worksheet with Answers

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

Unit 8: Going FurtherAdvanced: Precalculus PreviewCCSS G-SRT.D.11Advanced

Solving non-right triangles and finding their areas. 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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Law of Sines & Law of Cosines

Grade 10 · Math

Score___ / 12

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Learning goal: Advanced: Precalculus Preview · CCSS G-SRT.D.11

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

Example

Find the area of a triangle with sides 14 and 8 and an included angle of 58°, to 1 decimal place.

Answer: 47.5

RememberUnit circle and trig laws

(1, 0)30° (√3/2, ½)45° (√2/2, √2/2)60° (½, √3/2)(0, 1)(−1, 0)(0, −1)Point on the circle = (cos θ, sin θ)tan θ = sin θ ÷ cos θ180° = π radianssin² θ + cos² θ = 1Law of sines: a/sin A = b/sin BLaw of cosines: c² = a² + b² − 2ab cos C
  1. 1

    Find the area of a triangle with sides 10 and 17 and an included angle of 29°, to 1 decimal place.

    CAB101729°
    Answer
  2. 2

    In triangle ABC, A = 56°, B = 69° and a = 12. Use the law of sines to find b, to 1 decimal place.

    CABa = 12b = ?A = 56°, B = 69°
    Answer
  3. 3

    In triangle ABC, a = 7, b = 19 and C = 73°. Use the law of cosines to find c, to 1 decimal place.

    CABa = 7b = 19C = 73°c = ?
    Answer
  4. 4

    In triangle ABC, A = 37°, B = 79° and a = 14. Use the law of sines to find b, to 1 decimal place.

    CABa = 14b = ?A = 37°, B = 79°
    Answer
  5. 5

    In triangle ABC, a = 5, b = 17 and C = 100°. Use the law of cosines to find c, to 1 decimal place.

    CABa = 5b = 17C = 100°c = ?
    Answer
  6. 6

    Find the area of a triangle with sides 19 and 13 and an included angle of 63°, to 1 decimal place.

    CAB191363°
    Answer
  7. 7

    In triangle ABC, a = 19, b = 11 and C = 111°. Use the law of cosines to find c, to 1 decimal place.

    CABa = 19b = 11C = 111°c = ?
    Answer
  8. 8

    In triangle ABC, a = 15, b = 10 and C = 77°. Use the law of cosines to find c, to 1 decimal place.

    CABa = 15b = 10C = 77°c = ?
    Answer
  9. 9

    Find the area of a triangle with sides 12 and 15 and an included angle of 53°, to 1 decimal place.

    CAB121553°
    Answer
  10. 10

    In triangle ABC, a = 15, b = 5 and C = 37°. Use the law of cosines to find c, to 1 decimal place.

    CABa = 15b = 5C = 37°c = ?
    Answer
  11. 11

    Find the area of a triangle with sides 19 and 17 and an included angle of 48°, to 1 decimal place.

    CAB191748°
    Answer
  12. 12

    In triangle ABC, A = 69°, B = 26° and a = 7. Use the law of sines to find b, to 1 decimal place.

    CABa = 7b = ?A = 69°, B = 26°
    Answer

★ Challenge corner for fast finishers

Each interior angle of a regular polygon is 140°. How many diagonals does it have?

How did I do?

Teacher's comments

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

Answer key (click to show)
  1. 1.41.2
  2. 2.13.5
  3. 3.18.2
  4. 4.22.8
  5. 5.18.5
  6. 6.110
  7. 7.25.1
  8. 8.16
  9. 9.71.9
  10. 10.11.4
  11. 11.120
  12. 12.3.3
  13. ★27 (challenge corner)

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