Solving right triangles

Math

Definition

Finding all unknown sides and angles of a right triangle using trigonometric ratios (sine, cosine, tangent), the Pythagorean theorem, and the fact that the angles sum to 180°.

How It Works

  1. Identify the known sides and angles.
  2. Use SOH-CAH-TOA to set up an equation with the unknown.
  3. Use the Pythagorean theorem if two sides are known and you need the third.
  4. Find unknown angles using inverse trig functions or the angle sum property.
  5. Verify that all three angles sum to 180° and sides satisfy the Pythagorean theorem.

Examples

  • Given a right triangle with a 30° angle and hypotenuse 10: opposite = 5, adjacent = 5√3
  • A ladder leaning against a wall at 70° with the ground — find how high it reaches

Related Terms

Soh-cah-toa Pythagorean theorem Sine cosine tangent Special right triangles

Study This Concept

Practice solving right triangles with free review games in these units:

Trigonometry Unit 2: Right Triangle Trigonometry