SOHCAHTOA Calculator
Find a missing side or angle of a right triangle using SOH-CAH-TOA ratios.
About SOHCAHTOA Calculator
SOHCAHTOA is a mnemonic for the three primary trig ratios in a right triangle: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent. Given any angle and one side, you can find any other side; given two sides, you can find the angle.
Formula
SOH-CAH-TOA
sin θ = O/H, cos θ = A/H, tan θ = O/A
- O
- Opposite side
- A
- Adjacent side
- H
- Hypotenuse
- θ
- Acute angle
Worked example
With the default values below, SOHCAHTOA Calculator returns Result of 5.773503. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Solve forone of Missing side (given angle + one side), Missing angle (given two sides)
- Missing side (given angle + one side)
- Known angle (degrees)accepts 0.01–89.99
- 30
- Known side isone of Opposite, Adjacent, Hypotenuse
- Adjacent
- Known side lengthminimum 0.001
- 10
- Find which side?one of Opposite, Adjacent, Hypotenuse
- Opposite
- First side isone of Opposite, Adjacent, Hypotenuse
- Opposite
- First side lengthminimum 0.001
- 5
- Second side isone of Opposite, Adjacent, Hypotenuse
- Hypotenuse
- Second side lengthminimum 0.001
- 10
Results
- Result
- 5.773503
- Ratio used
- opp = adj × tan(30°) = 10 × 0.57735
Step by step
- 1Identify the ratio= opp = adj × tan(30°) = 10 × 0.57735
- 2Result= opposite = 5.77350269
Assumptions and limits
- The result is derived only from the 9 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What does SOHCAHTOA stand for?
SOH = Sine is Opposite over Hypotenuse, CAH = Cosine is Adjacent over Hypotenuse, TOA = Tangent is Opposite over Adjacent.
Can I use SOHCAHTOA for non-right triangles?
No — these ratios apply only to right triangles. For oblique triangles use the Law of Sines or Law of Cosines.