How do you use SOHCAHTOA to find a side or angle?
Short answer
In a right-angled triangle, sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse and tan θ = opposite ÷ adjacent. Label the sides relative to the angle, pick the ratio that uses the two sides involved, then rearrange. To find an angle, use the inverse function (sin⁻¹, cos⁻¹ or tan⁻¹).
Step by step
- Label the hypotenuse (opposite the right angle), the opposite side (facing the angle) and the adjacent side (next to the angle).
- Identify the side you know and the side you want, or the two sides you know.
- Choose SOH, CAH or TOA, the one that contains those two sides.
- To find a side, rearrange and calculate. To find an angle, use the inverse function on your calculator.
- Check your calculator is in degrees.
Worked example
Angle 35°, hypotenuse 12 cm. Find the opposite side.
- Opposite and hypotenuse, so use SOH
- sin 35° = x ÷ 12
- x = 12 × sin 35° = 6.88 cm (3 s.f.)
Common mistakes
- Labelling opposite and adjacent from the wrong angle.
- Using a calculator set to radians.
- Dividing instead of multiplying when the unknown is on top of the fraction.
Useful for:GCSEIGCSEWAECBEPCMatric
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