Math

Solving right triangles.

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 · 5 phases

Step by step.

  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

Real-world.

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

Tangled up with.

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

1 unit use this concept.

Trigonometry Right Triangle Trigonometry →