Finding an Angle in a Right Angled Triangle

We can find an unknown angle in a right-angled triangle, as long as we know the lengths of two of its sides.

Use Sine, Cosine or Tangent!

Use SOHCAHTOA to help you, like this:

How to Finding an Angle in a Right Angled Triangle

1. find the names of the two sides we know

Right Angled Triangle
  • Adjacent is adjacent to the angle,
  • Opposite is opposite the angle,
  • Hypotenuse is The longest side.

2. Find which one of Sine, Cosine or Tangent to use:

SOH… Sine: sin(θ) = Opposite / Hypotenuse

CAH… Cosine: cos(θ) = Adjacent / Hypotenuse

TOA Tangent: tan(θ) = Opposite / Adjacent

3. Put the values into equation  

4. Solve that equation and find the value of θ

Example

Right Angled Triangle Example

Sin (θ) = Opposite / Hypotenuse = 3 / 6 = 0.5

Sin (θ) = 0.5,

then θ = sin-1(0.5) = 30o

Learn More

Consecutive Interior Angles

Angles of Elevation & Depression

Irregular Polygon

Lines of Symmetry of Plane Shapes

Algebra Index

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