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Year 9 · Trigonometry
Trigonometric ratios: find a side
In a right-angled triangle, sine, cosine and tangent link an angle to two sides: SOH CAH TOA.
How to do it
- Label the sides from the angle: Opposite, Adjacent, Hypotenuse.
- Pick the ratio that uses the side you know and the side you want.
- Finding an angle: use the inverse (sin⁻¹, cos⁻¹, tan⁻¹).
Worked example
Find x, to one decimal place.
x is opposite the 60° angle and 6 is adjacent. tan 60° = x ÷ 6, so x = 6 × tan 60° ≈ 10.4.
Answer: 10.4
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Watch outThe hypotenuse is opposite the right angle; the opposite side is across from the angle you are using.
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