Edexcel International GCSE Mathematics A · 4MA1
Right-angled trigonometry
Sine, cosine and tangent connect an acute angle with side ratios in a right-angled triangle. Opposite and adjacent depend on the chosen angle; the hypotenuse is always opposite the right angle. Draw and label the triangle before using a calculator.
Key method
sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Use degree mode when angles are given in degrees.
Worked example
A right triangle has hypotenuse 10 cm and an acute angle of 30°. Find the opposite side.
- The known hypotenuse and required opposite side select sine.
- Write sin 30° = x/10.
- Multiply by 10: x = 10 × 0.5.
Answer and interpretation
5 cm.
Common mistake
Using the inverse sine button to find a side confuses finding an angle with finding a length.
Practise independently
Opposite = 6 and adjacent = 8. Find the angle to one decimal place.
Check your answer
θ = tan⁻¹(6/8) = 36.9°.
Syllabus connection
This lesson develops trigonometric ratios within the geometry area. Start with the worked method, attempt the independent question without looking at its answer, then explain any correction in your own words. Check the official specification for your tier’s full requirements.
Related resources
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