Geometry
Trigonometric ratios (SOH-CAH-TOA)
In a right triangle, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent. Choosing the ratio is a matter of labelling the sides relative to the angle you are given.
Why it matters
Right-triangle trig underpins vectors, the unit circle, and every physics problem involving components. It is also one of the highest-frequency SAT geometry topics.
Worked example
A ladder reaches 6 m up a wall at 65° to the ground. How long is the ladder?
- 1Label relative to 65°. 6 m is opposite; the ladder is the hypotenuse
- 2Choose the ratio. sine uses opposite and hypotenuse
- 3Set up. sin 65° = 6 / L
- 4Rearrange. L = 6 / sin 65° ≈ 6 / 0.9063
Answer: L ≈ 6.62 m
Common mistakes
- Leaving the calculator in radians for a degree question.
- Labelling opposite and adjacent before identifying the reference angle.
- Rounding intermediate values and carrying the error forward.
How to check your answer
- The hypotenuse must be the longest side — if your answer is shorter than a leg, the setup is wrong.
- Sine and cosine of an acute angle are always between 0 and 1.
Related topics
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