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Wize High School Grade 10 Math Textbook > Trigonometry of Right Triangles

Solving Right Triangles

Finding Angle Measures in a Right TrianglePrevious Section
Right Triangle Word ProblemsNext Section
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Solving a Right Triangle

If we are asked to solve a right triangle, we need to find all missing angles and side lengths.

Finding a side length

  • If you know 2 of the side lengths ➡ use Pythagorean's Theorem to find the remaining third side
  • If you know 1 of the side lengths and 1 of the angles ➡ use SOH CAH TOA to find the remaining sides

Finding an angle

  • If you know the measurement of 1 of the non-right angles ➡ use the fact that the interior angles add up to 180°\bcfi{180\degree}
  • If you know the measurement of 2 of the side lengths ➡ use SOH CAH TOA and sin⁡−1\bcfi{\sin^{-1}}, cos⁡−1\bcfi{\cos^{-1}} and tan⁡−1\bcfi{\tan^{-1}} to find the angle

Practice: Solving a Right Triangle

Solve the triangle △ABC\triangle ABC.

Practice: Solving a Right Triangle

△XYZ\triangle XYZ has a right angle at ∠X\angle X. XY=7cmXY=7cm and XZ=5cmXZ=5cm. Solve the triangle.