Choosing sine, cosine or tangent (SOH CAH TOA)
Label the sides from the angle, then pick the ratio that uses the two you have.
The common mistake
Labelling opposite and adjacent from the wrong angle, or from the right angle.
Instead: Stand at the given angle: opposite is across from it, adjacent touches it, hypotenuse is longest. Then choose SOH, CAH or TOA.
Worked example with Guide me
Angle 30°, hypotenuse 12. Find the side opposite the angle.
- Sugar · Which sides are involved?Student · Opposite and hypotenuse.
- Sugar · Which ratio?Student · Sine: sin 30° = opp/12.
- Sugar · Solve.Student · opp = 12 × 0.5 = 6.
Answer: 6
Try 3 practice questions
1. Angle 60°, hypotenuse 10 — adjacent side?
Show answer
5 (cos 60° = 0.5)
2. Angle 45°, adjacent 7 — opposite side?
Show answer
7 (tan 45° = 1)
3. Opposite 3, hypotenuse 6 — the angle?
Show answer
30°
Quick answers
- What is the most common mistake with choosing sine, cosine or tangent (soh cah toa)?
- Labelling opposite and adjacent from the wrong angle, or from the right angle.
- How do I get choosing sine, cosine or tangent (soh cah toa) right?
- Stand at the given angle: opposite is across from it, adjacent touches it, hypotenuse is longest. Then choose SOH, CAH or TOA.
- Can you show a worked example?
- Angle 30°, hypotenuse 12. Find the side opposite the angle. 6
Related concepts
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