What you need to know
Geometry questions reward a clear chain of reasons. Draw or annotate the diagram, decide which relationship applies, and keep enough working to show why each angle, length or area result follows.
- Use standard angle facts and geometric properties with reasons.
- Apply Pythagoras in right-angled triangles.
- Choose sine, cosine or tangent from the known and required sides.
- Use sine/cosine rules when the triangle is not right-angled and the data fits.
Key mathematics
Pythagoras
a^2+b^2=c^2
c is the hypotenuse in a right-angled triangle.Right-triangle trig
\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}},\quad \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}},\quad \tan\theta=\frac{\text{opposite}}{\text{adjacent}}
Label sides relative to the chosen angle.Worked example
If a right triangle has adjacent side 8 and hypotenuse 10, then $$\cos\theta=\frac{8}{10}=0.8.$$ Hence $\theta=\cos^{-1}(0.8)\approx36.9^\circ$.
EXAM TECHNIQUE
Exam tips
- Mark the right angle and label opposite/adjacent/hypotenuse before choosing a trig ratio.
- Keep calculator mode in degrees unless radians are explicitly required.
- Give geometric reasons where the question asks you to show or prove a result.
WATCH OUT
Common mistakes
- Using the wrong side as the hypotenuse.
- Rounding a length too early before using it in the next part.
- Using a right-triangle trig ratio in a triangle that is not right-angled without first creating a right triangle.
Frequently asked questions
How do I choose sine, cosine or tangent?
Identify the sides you know and need relative to the angle, then choose the ratio containing those sides.
When can I use Pythagoras?
Only in a right-angled triangle.
Why should I avoid early rounding?
Rounded intermediate values can create avoidable final-answer errors, especially in multi-step geometry problems.