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Mathematics · Grade 10

Right Triangles and Trigonometric Ratios

Learners use the Pythagorean theorem and its converse to find lengths and classify triangles, and learn the 45°–45°–90° and 30°–60°–90° relationships. They see sine, cosine and tangent as ratios that similar right triangles share, use them and their inverses to find sides and angles, connect sine and cosine of complementary angles, and solve angle-of-elevation and depression problems. An optional honors lesson introduces the Law of Sines, the Law of Cosines and the area formula ½ab sin C.

  • 5 lessons
  • About 135 minutes
  • Right triangles and trigonometry check: 11 questions
  • Ways to answer: fill in the blanks, choose an answer, match pairs, type a number, put in order and sort into groups
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What learners will discover

  • Use the Pythagorean theorem and its converse to find lengths and classify triangles as acute, right or obtuse, and apply the special right triangle relationships.
  • Explain trigonometric ratios as properties of similar right triangles and use sine, cosine and tangent to find unknown side lengths.
  • Use inverse trigonometric ratios to find unknown angles and apply the relationship sin θ = cos(90° − θ).
  • Model and solve applied problems involving angles of elevation and depression and other right-triangle situations, with appropriate rounding.

Lessons

  1. The Pythagorean theorem and special right triangles 7 steps5 practiceabout 28 min
  2. Trigonometric ratios 7 steps5 practiceabout 30 min
  3. Finding angles and complementary angles 6 steps4 practiceabout 27 min
  4. Elevation, depression and modeling 7 steps4 practiceabout 32 min
  5. Going further (honors): beyond right triangles 4 steps1 practiceabout 18 min
  6. Right triangles and trigonometry check 11 questions at the end

Keep exploring

More 10th grade math

Guide for grown-ups