SOHCAHTOA: Sine, Cosine and Tangent Explained with Examples
Remember sine, cosine and tangent with SOHCAHTOA, choose the right ratio, and solve for a side and an angle in two worked examples.
SOH-CAH-TOA
- sin θ = opposite / hypotenuse
- cos θ = adjacent / hypotenuse
- tan θ = opposite / adjacent
Label the sides from the angle you are using.
Pick the right ratio
- Opposite + hypotenuse: sine
- Adjacent + hypotenuse: cosine
- Opposite + adjacent: tangent
Two sides in the problem decide the ratio.
Example 1
Find x. The angle is 30°, the hypotenuse is 10, and x is opposite the angle.
- Opposite and hypotenuse: use sine.
- sin 30° = x / 10, and sin 30° = 0.5
x = 10 × 0.5 = 5
Example 2
Find θ. The opposite side is 3 and the adjacent side is 4.
- Opposite and adjacent: use tangent.
- tan θ = 3 / 4, so θ = tan⁻¹(0.75)
θ ≈ 36.9°
Common mistake
tan θ = opposite / hypotenuse
Tangent uses the two legs: opposite over adjacent.
Opposite and adjacent swap when you switch to the other angle.
Set your calculator to degrees, not radians.
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