Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Right Angled Trigonometry — using sine, cosine and tangent to find missing sides and angles — to become a reliable source of marks instead of a mnemonic 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 Trigonometry unit in Cambridge IGCSE Mathematics (0580/0607). Whenever a question involves a right-angled triangle and a missing side or angle, examiners expect you to label opposite, adjacent and hypotenuse correctly and apply SOHCAHTOA with clear working. This guide explains exactly what the ratios cover, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• SOHCAHTOA applies only to right-angled triangles: sin = O/H, cos = A/H, tan = O/A.
• Label opposite, adjacent and hypotenuse relative to the angle you are using — they swap if you change angle.
• To find a side, pick the ratio linking the known and unknown sides; to find an angle, use sin⁻¹, cos⁻¹ or tan⁻¹.
• Always state the ratio, show substitution and give the final answer with correct units or degrees.

What is Right Angled Trigonometry in Cambridge IGCSE Maths?

Right Angled Trigonometry is the use of sine, cosine and tangent ratios to relate sides and angles in a right-angled triangle. In Cambridge IGCSE Mathematics it is used to find a missing side when one side and one acute angle are known, to find an angle when two sides are known, and as the first step in elevation, depression and bearing problems.

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
Opposite / adjacent	Sides relative to the chosen angle	”Calculate the length of BC” with angle at A
Hypotenuse	Longest side, opposite the right angle	Always H in SOHCAHTOA
Finding a side	Choose ratio; substitute; rearrange	”Work out the height of the triangle”
Finding an angle	Use inverse trig on calculator	”Find the size of angle θ”

How to use SOHCAHTOA — step by step

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

1. Identify the right angle and mark the angle you are working with.
2. Label O, A and H relative to that angle.
3. Pick the ratio that uses the two sides you know (or know and want).
4. Write the equation — e.g. sin 35° = opp/hyp — and substitute.
5. Rearrange and calculate; use sin⁻¹, cos⁻¹ or tan⁻¹ for angles.
6. Check: angles in a triangle sum to 180°; the hypotenuse is the longest side.

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 does the question want?

Students lose marks by labelling opposite and adjacent from the wrong angle or by using the wrong ratio. Use the diagram to decide.

Situation	What to do	Typical signal words
Missing side, angle known	sin/cos/tan with known angle	”Calculate the length of…”, “Work out the height”
Missing angle, sides known	Inverse trig function	”Find the size of angle…”, “Calculate θ”
Angle of elevation / depression	Draw a right triangle from the diagram	”angle of elevation”, “from the horizontal”
Two-step problem	Trigonometry then Pythagoras (or vice versa)	Ladder, flagpole, building problems

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

Most lost marks come from misreading the command word or labelling sides from the wrong angle. 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	Find a side or angle with full method	”Work out the length of the ladder.”
Show that	Prove a given result — method earns marks	”Show that the angle of elevation is 38°.”
Write down	State a value; minimal working (usually 1 mark)	“Write down the value of sin 30°.”
Give your answer correct to …	Round as instructed	”Give your answer correct to 1 decimal place.”
Find the angle of elevation	Draw triangle; use tan or sin	”Find the angle of elevation of the top of the tower.”

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

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

1. “In triangle ABC, angle C = 90°, angle A = 40° and AC = 12 cm. Work out the length of BC.” Relative to A: opp = BC, adj = AC. tan 40° = BC/12 → BC = 12 tan 40° ≈ 10.1 cm. Mark-scheme reward: correct ratio chosen, substitution shown.
2. “A ladder of length 6 m leans against a wall, making an angle of 65° with the ground. Show that the foot of the ladder is 2.54 m from the wall.” cos 65° = adj/6 → adj = 6 cos 65° ≈ 2.54. Reward: full working — stating 2.54 alone scores nothing on “Show that”.
3. “From a point 50 m from the base of a tower, the angle of elevation of the top is 32°. Calculate the height of the tower.” tan 32° = h/50 → h = 50 tan 32° ≈ 31.2 m. Reward: right triangle drawn or implied, tan ratio used.

When you can recognise the wording instantly, work the full set on the Trigonometry topical past paper questions and 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, where angles are measured clockwise from North, and underpins 3D Trigonometry when right triangles appear inside cuboids and prisms. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Labelling opposite and adjacent from the wrong angle.
• Using sin when tan is needed (or vice versa).
• Forgetting to use inverse trig (sin⁻¹) when finding an angle.
• Calculator in radians instead of degrees.
• Rounding too early and losing accuracy marks on multi-step questions.

When you need more support

If right-angled trigonometry questions keep tripping you up — especially elevation and depression — work through the Trigonometry topical past paper questions and 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 straightforward once you label sides correctly. Marks are lost when students pick the wrong ratio or label opposite and adjacent from the wrong angle.

What does SOHCAHTOA stand for? Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent — each applies to a right-angled triangle.

How do I find an angle using trigonometry? Pick the ratio linking the two known sides, then use sin⁻¹, cos⁻¹ or tan⁻¹ on your calculator.

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 any elevation problems you got wrong before moving on.

Ready to master Cambridge IGCSE Maths Right Angled Trigonometry?

Start with the Right Angled Trigonometry subtopic page, then book a free trial with a Cambridge IGCSE Maths specialist to turn Right Angled Trigonometry into guaranteed marks.

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