Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Right Angled Trigonometry — sine, cosine and tangent ratios in right-angled triangles — to become a reliable source of marks instead of SOHCAHTOA they only half-remember.
What query it owns: how to understand and revise Right Angled Trigonometry in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Right Angled Trigonometry revision-guide angle, while Tutopiya’s Right Angled Trigonometry subtopic page owns the learning resource and the free Right Angled Trigonometry quiz owns the practice.

Right Angled Trigonometry is the foundation of the entire Trigonometry unit in Cambridge IGCSE Mathematics (0580/0607). Whenever a question involves a right-angled triangle, examiners expect you to choose the correct ratio — sin, cos or tan — label sides relative to the correct angle, and use your calculator accurately. This guide explains exactly what the subtopic covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• SOHCAHTOA links each ratio to opposite, adjacent and hypotenuse relative to a chosen acute angle.
• The hypotenuse is always opposite the right angle and is the longest side.
• To find an angle, use sin⁻¹, cos⁻¹ or tan⁻¹ — check your calculator is in degree mode.
• Draw the triangle, mark the angle you are using, and label O, A and H before choosing a ratio.

What is Right Angled Trigonometry in Cambridge IGCSE Maths?

Right Angled Trigonometry uses the ratios sin θ = O/H, cos θ = A/H and tan θ = O/A to find missing sides or angles in right-angled triangles. In Cambridge IGCSE Mathematics it appears in elevation and depression problems, ladder-and-wall diagrams, and as the first step before bearings and 3D trigonometry.

You can read the full explanation, worked examples and notes on Tutopiya’s Right Angled Trigonometry subtopic page before you attempt questions.

The core ideas you must master

These four ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
Label sides	O, A, H relative to θ	”Calculate the length of BC”
Find a side	Multiply or divide by sin/cos/tan	”Work out the height of the tower”
Find an angle	Use inverse trig	”Find the angle of elevation”
Pythagoras link	Use when no angle is involved	”Find the hypotenuse first”

How to use SOHCAHTOA — step by step

The safest method works for every right-angled triangle question.

1. Sketch the triangle and mark the right angle.
2. Choose the acute angle θ that connects the sides you know and want.
3. Label O, A and H relative to θ — not relative to the other acute angle.
4. Pick sin, cos or tan — which ratio uses the two sides you need?
5. Write the equation, substitute and solve. For angles, use the inverse function.
6. Check: calculator in degrees; answer has correct units and rounding.

Once you have worked through a few, test yourself with the free Right Angled Trigonometry quiz — it tells you fast whether the method has actually stuck.

Finding a side vs finding an angle: which approach?

Students lose marks by labelling sides from the wrong angle or using the wrong ratio. Use what you know to decide.

Situation	What to do	Typical signal words
Two sides known, need third	Pythagoras if no angle given	”right-angled triangle”, no angle stated
Angle and one side known	SOHCAHTOA	”angle of elevation”, “angle marked θ”
Need an angle	Inverse sin/cos/tan	”Find angle ABC”
Horizontal and vertical	tan often links them	”height”, “ladder”, “tower”

Right Angled Trigonometry in past-paper wording: command words that matter

Most lost marks come from wrong labelling or degree/radian mode errors. These are the command words you will see and what each one demands.

Command word / phrase	What the question wants	Typical stem
Calculate / Work out	Full method with ratio stated	”Work out the length of the ladder.”
Angle of elevation / depression	Draw horizontal reference line	”The angle of elevation of the top is 35°.”
Give your answer correct to …	Round as instructed	”Give your answer correct to 1 decimal place.”
Show that	Prove a given length or angle	”Show that BC = 8.7 m correct to 1 d.p.”
Write down	One-step calculator use	”Write down the value of sin 42°.”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just SOHCAHTOA — is what method marks reward. Here is how three real-style stems are answered.

1. “In triangle ABC, angle B = 90°, AB = 5 cm and angle A = 37°. Work out the length of BC.” Relative to A: BC is opposite, AB is adjacent → tan 37° = BC/5 → BC = 5 tan 37° ≈ 3.77 cm. Mark-scheme reward: correct ratio choice and substitution.
2. “A ladder of length 6 m leans against a wall, making an angle of 68° with the ground. Work out how high up the wall it reaches.” Height is opposite, ladder is hypotenuse → sin 68° = h/6 → h = 6 sin 68° ≈ 5.56 m. Reward: opposite and hypotenuse identified correctly.
3. “From a point 40 m from the base of a tower, the angle of elevation of the top is 52°. Work out the height of the tower.” tan 52° = h/40 → h = 40 tan 52° ≈ 51.2 m. Reward: horizontal distance used as adjacent side.

When you can recognise the wording instantly, work through related topics starting with Bearing and take the Right Angled Trigonometry quiz to lock the method in.

How Right Angled Trigonometry connects to the rest of Trigonometry

SOHCAHTOA feeds directly into Bearing problems, where you draw north lines and right triangles. It pairs with Pythagoras Theorem when you need a third side before applying a ratio. Later, Sine Rule and Cosine Rule extend trigonometry to non-right triangles. The Cambridge IGCSE Maths resource hub links all subtopics.

Common mistakes students make

• Labelling opposite and adjacent from the wrong acute angle.
• Using sin when tan is needed (or vice versa).
• Calculator in radian mode instead of degrees.
• Rounding too early in multi-step problems.
• Applying SOHCAHTOA to a triangle that is not right-angled.

When you need more support

If elevation or ladder questions keep tripping you up, work through the Right Angled Trigonometry quiz to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Is Right Angled Trigonometry hard in Cambridge IGCSE Maths? The ratios are fixed — difficulty comes from labelling sides correctly and choosing the right ratio for the diagram.

What does SOHCAHTOA stand for? Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent — all relative to the angle you are using.

When should I use Pythagoras instead of trigonometry? When you know two sides and need the third with no angle involved, or when you need the hypotenuse before applying a ratio.

How do I revise Right Angled Trigonometry effectively? Read the subtopic notes, label O, A and H on every diagram, then take the Right Angled Trigonometry quiz. Revisit elevation problems you got wrong before moving on.

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