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Trigonometry practice: SOHCAHTOA questions

SOHCAHTOA gives the three trigonometry ratios in a right-angled triangle: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, tangent equals opposite over adjacent. Label the sides from the marked angle, pick the ratio using the two sides you know and want, then solve.

SOHCAHTOA is the memory aid for the three trigonometric ratios in a right-angled triangle: Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.

Year 9GCSE FoundationGCSE Higher

The method, step by step

  1. Label the triangle. Hypotenuse opposite the right angle, opposite across from the marked angle, adjacent next to it.
  2. Note which two sides matter. One you know, one you want.
  3. Pick the ratio. Whichever of SOH, CAH or TOA uses exactly those two sides.
  4. Substitute and solve. Rearrange for the unknown before reaching for the calculator.

Worked example

A right-angled triangle has a 30° angle with an opposite side of 7cm. Find the hypotenuse.
Opposite and hypotenuse are involved, so use SOH: sin 30° = opposite ÷ hypotenuse.
sin 30° = 0.5 exactly, so 0.5 = 7 ÷ hypotenuse.
Rearrange: hypotenuse = 7 ÷ 0.5.
The hypotenuse is 14cm

Common mistakes

Labelling opposite and adjacent from the right angle rather than from the marked angle.

Leaving the calculator in radians. For GCSE it must be in degrees.

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