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Right-Angled Trigonometry (F)

Use higher-tier trigonometry to find sides and angles in right-angled triangles with sine, cosine and tangent, using SOH CAH TOA and careful labelling.

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Fascinating Fact:

In a triangle sketch, label sides from the angle: hypotenuse equals longest, opposite equals across from the angle, adjacent equals next to the angle. This choice decides sine, cosine, or tangent.

In GCSE Maths, trigonometry links angles and lengths in right-angled triangles. You’ll choose sine, cosine or tangent with SOH CAH TOA, find unknown sides or angles, and round answers sensibly.

Key Terms

Hypotenuse: The longest side of a right-angled triangle, opposite the 90° angle.
Opposite: The side directly across from the chosen angle (not the right angle).
Adjacent: The side next to the chosen angle, but not the hypotenuse.

Frequently Asked Questions (Click to see answers)

How do I choose sine, cosine or tangent?

Identify the two sides you are using relative to the angle: SOH (opposite/hypotenuse), CAH (adjacent/hypotenuse), or TOA (opposite/adjacent). Pick the ratio that matches those sides.

How do I find a missing angle with trigonometry?

Use an inverse function. For example, if opposite and hypotenuse are known, angle θ = sin⁻¹(opposite ÷ hypotenuse). Ensure your calculator is in degrees.

What’s the difference between adjacent and opposite?

Both are defined by the chosen angle: the opposite is across from it; the adjacent touches it (but is not the hypotenuse). Always choose the reference angle first.