Free · Algebra and geometric relations

Angle Ratios and Right Triangle Relations

Explore six trigonometric ratios alongside editable right-triangle measurements.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked example, Side c = 5, Area = 6.

sin θ, cos θ, tan θ and their reciprocals; c²=a²+b²

Worked example

Enter these known values and leave the other values blank.

Side a
3 cm
Side b
4 cm
Side c
5 cm
Angle α
36.87 deg
Angle β
53.13 deg
Area
6 cm²

Assumptions and limitations

  • Triangle lengths are positive and its two non-right angles are acute.
  • General angle ratios are periodic. Tangent and secant are undefined at odd quarter turns; cotangent and cosecant at half turns. Inverse functions select principal branches.
  • Auxiliary degree numbers use degree-valued presentation units, preventing doubled conversion in angle notes.

Common questions

How do I use this relation?

Choose the relevant mode and enter independent known quantities. Leave a missing value empty where the control permits an inverse.

What do the displayed numbers mean?

The result follows the stated mathematical model. All dimensions must use consistent units; available unit selectors handle conversions.

References

The auxiliary angle_degrees_print and base_angle formulas produce degree-valued reference numbers. Their captured SI-radian selectors converted those values twice in dynamic notes. These two hidden presentation selectors now use degree-valued reference conversions; the physical angle selector remains unchanged. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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