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Year 10 · Trigonometry

Trigonometric ratios: find an angle

In a right-angled triangle, sine, cosine and tangent link an angle to two sides: SOH CAH TOA.

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How to do it

  1. Label the sides from the angle: Opposite, Adjacent, Hypotenuse.
  2. Pick the ratio that uses the side you know and the side you want.
  3. Finding an angle: use the inverse (sin⁻¹, cos⁻¹, tan⁻¹).

Worked example

Find the angle θ, in degrees, to one decimal place.
θ is between the adjacent side (9) and the hypotenuse, and the opposite side is 10.7. tan θ = opposite ÷ adjacent = 10.7 ÷ 9, so θ = tan⁻¹(1.189) ≈ 49.9°.
Answer: 49.9

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The hypotenuse is opposite the right angle; the opposite side is across from the angle you are using.

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