Trigonometry basics
Use the trigonometric ratios sin, cos, and tan in right-angled triangles to find unknown sides and angles, including setting up the correct ratio for a given problem
What a learner can do afterwards
- Identify which trigonometric ratio to use (SOH CAH TOA) based on the known and unknown sides
- Calculate an unknown side using sin, cos, or tan and a known angle
- Find an unknown angle using the inverse trigonometric function (e.g. tan⁻¹)
The lesson
Right triangles have three sides with special names, based on which angle you are looking at. The hypotenuse is the longest side, always across from the right angle. The other two sides are the opposite side (across from your chosen angle) and the adjacent side (next to your chosen angle, not the hypotenuse).
Three ratios connect the sides to the angle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, and tan θ = opposite/adjacent. The letters SOH CAH TOA help you remember which sides go with which ratio.
A ramp is 8 metres long and rises from the ground at 30°. The height is opposite the 30° angle, and the ramp length is the hypotenuse, so use sin. Sin(30°) = 0.5, so height = 8 × 0.5 = 4 metres.
If you know two sides but not the angle, use the inverse function to work backwards. For example, if sin θ = 0.5, then θ = sin⁻¹(0.5) = 30°.
SOH CAH TOA tells you which ratio to use, then multiply or use the inverse function to find the missing side or angle.
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