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Trigonometry (SOHCAHTOA) - Edexcel GCSE Higher Maths

Typically 3-6 marks per paper, concentrated on Papers 2 and 3 · Spec 1MA1

Right-angled trigonometry is spec reference G20 on Edexcel's 1MA1: the three ratios sine, cosine and tangent, used to find a missing side or a missing angle in a triangle that contains a 90∘90^\circ angle. G20 is common content, so a Foundation candidate meets the same three ratios. What changes at Higher tier is the packaging. Spec reference G21, the exact values of sin and cos at 0, 30, 45, 60 and 90∘90^\circ and of tan at 0, 30, 45 and 60∘60^\circ, is Higher only, and once the triangle has no right angle you are into G22, the sine and cosine rules, which is a different page and a different decision.

Papers 2 and 3 are the calculator papers, and that is where most SOHCAHTOA marks sit: a single triangle for 2-3 marks in the first half, then a longer problem for 4-5 marks where the length you find in one triangle becomes the known side in the next. The contexts repeat from series to series, and they are worth recognising on sight: a ladder against a vertical wall, an angle of elevation from a point on level ground, an angle of depression from a cliff top or a lighthouse, a ramp, the diagonal of a rectangle. Every figure carries the words 'Diagram NOT accurately drawn', so a protractor scores nothing. On Paper 1 the ratios still appear, but only at angles whose exact values you are expected to know.

The method mark goes on a correct trigonometric statement, so write tan⁡42∘=18x\tan 42^\circ = \frac{18}{x} down before you touch the calculator: even if the rearrangement then goes wrong, that mark is banked. The accuracy mark is lost in two predictable places. One is multiplying when you should divide, which happens whenever the unknown sits underneath. The other is rounding a middle value to 1 decimal place and feeding it into the next stage, which drags the final answer outside the range the mark scheme allows. Practise labelling opposite and adjacent from the angle you have marked rather than from where the sides happen to sit on the page.

Worked example

A vertical mast MB stands on horizontal ground, with B at the foot of the mast. P and Q are two points on the ground, on opposite sides of the mast, so that P, B and Q lie on a straight line. The mast is 18 m tall. The angle of elevation of the top M from P is 42∘42^\circ and the angle of elevation of M from Q is 31∘31^\circ. Work out the distance PQ. Give your answer to the nearest metre.
[4 marks]
  1. Triangle MBP has its right angle at B. From P, the mast MB is opposite the 42∘42^\circ angle and BP is adjacent to it, so use tan: tan⁡42∘=18BP\tan 42^\circ = \frac{18}{BP}.
    M1: correct ratio for the first triangle, with 18 as the opposite side
  2. The unknown is underneath, so swap it with the tan⁡42∘\tan 42^\circ: BP=18tan⁡42∘=19.991…BP = \frac{18}{\tan 42^\circ} = 19.991\ldots m. Keep that on the display.
    M1: rearranging to BP = 18 divided by tan 42, not 18 multiplied by it
  3. Triangle MBQ is right angled at B in exactly the same way: tan⁡31∘=18BQ\tan 31^\circ = \frac{18}{BQ}, so BQ=18tan⁡31∘=29.957…BQ = \frac{18}{\tan 31^\circ} = 29.957\ldots m.
    A1: second length correct, 29.9 to 30.0
  4. B lies between P and Q, so the two lengths add: PQ=19.991+29.957=49.94…PQ = 19.991 + 29.957 = 49.94\ldots, which is 50 m to the nearest metre.
    A1: 50 m, from the unrounded values rather than from 20 and 30

Practice questions

These are original questions in Edexcel 1MA1 Higher style. There are no diagrams, so each triangle is described in full: sketch it from the words, mark the right angle, then choose the ratio. Right-angled trigonometry is mostly a calculator-paper skill, so use a calculator in degree mode, hold the full display value between stages, and round only where the question tells you to.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

  1. Question 1 Warm-up [1 mark]
    You know one acute angle of a right-angled triangle and the length of the side adjacent to that angle. You want to find the hypotenuse. Which ratio connects those two sides?
    Answer options for question 1
  2. Question 2 Warm-up [2 marks]
    Triangle ABC has a right angle at C. AC = 3 cm and BC = 4 cm. Work out the size of angle BAC. Give your answer in degrees to 1 decimal place.
  3. Question 3 Exam pace [3 marks]
    The top of a lighthouse is 36 m above sea level. A boat is at sea, 120 m horizontally from the foot of the lighthouse. Work out the angle of depression of the boat from the top of the lighthouse. Give your answer in degrees to 1 decimal place.
  4. Question 4 Exam pace [3 marks]
    A straight playground slide runs down to level ground. The slide is 3.5 m long and its top is 1.4 m vertically above the ground. Work out the angle the slide makes with the ground. Give your answer in degrees to 1 decimal place.
  5. Question 5 Stretch [4 marks]
    A straight wire 25 m long runs from the top of a vertical mast to a point on horizontal ground. The wire makes an angle of 62 degrees with the ground. Work out the height of the mast and the distance of the ground anchor from the foot of the mast. Give each answer in metres to 1 decimal place.
  6. Question 6 Stretch [4 marks]
    Triangle ABC has a right angle at B. Its area is 30 square centimetres and AB = 10 cm. Work out the size of angle BAC. Give your answer in degrees to 1 decimal place.

Common mistakes examiners see

  • Labelling the sides by where they sit on the page. In a triangle with the right angle at B and the marked angle at A, students call AB the opposite because it looks like the upright, then use sin where cos was needed.

    Mark the right angle first and call the side facing it the hypotenuse. Then work from the angle the question gives you: the side facing that angle is the opposite, the remaining side is the adjacent. Relabel from scratch whenever the question moves to a different angle.

  • Reading cos⁡55∘=7x\cos 55^\circ = \frac{7}{x} and writing x=7cos⁡55∘=4.01x = 7 \cos 55^\circ = 4.01 instead of x=7cos⁡55∘=12.2x = \frac{7}{\cos 55^\circ} = 12.2.

    When the unknown is on the bottom of the fraction, it swaps places with the trig value: x=7cos⁡55∘x = \frac{7}{\cos 55^\circ}. Then size-check it, because the hypotenuse has to come out longer than 7, not shorter.

  • Pressing sin instead of sin⁡−1\sin^{-1} when the answer is an angle, so sin⁡x=0.6\sin x = 0.6 gives 0.0105 rather than 36.9∘36.9^\circ.

    An answer in degrees needs SHIFT and then sin, cos or tan. Check the display shows a small D before the paper starts as well: a calculator left in radians turns every angle answer into a decimal below 1.6, which is a warning sign worth learning.

  • Rounding a middle value, writing 4.5 for a length the calculator gave as 4.4623, then using 4.5 in the second triangle so the final answer falls outside the mark scheme's accepted range.

    Store the unrounded value or use the ANS key, and round once on the final line. Still write the intermediate value down to at least 3 significant figures so the examiner can follow the method marks.

  • Using sin, cos or tan in a triangle with no right angle, for example writing sin⁡40∘=x9\sin 40^\circ = \frac{x}{9} in a triangle whose angles are 40, 65 and 75∘75^\circ.

    Find the 90∘90^\circ angle before choosing a ratio. If there is not one, the question wants the sine rule or the cosine rule, or it wants you to drop a perpendicular first and create a right-angled triangle to work in.

Frequently asked questions

Do I get the trigonometry formulae in the Edexcel exam?
The Higher tier exam aid issued with the 2025 to 2027 papers lists the three right-angled triangle ratios alongside the sine rule, the cosine rule and the area of a triangle formula. It gives you the ratios but not the choice, and choosing between sin, cos and tan is the part being assessed. The exact values at 30, 45 and 60 degrees are not on the sheet, so those still have to be learnt.
Is SOHCAHTOA on the Foundation paper too?
Yes. Right-angled trigonometry is spec reference G20, which is common content across both tiers, so Foundation candidates use the same three ratios. Higher tier adds the exact values (G21) and the sine and cosine rules (G22), and tends to bury the ratio inside a longer problem where one answer feeds the next.
How many marks is right-angled trigonometry worth on Edexcel Higher?
One triangle asking for one side or one angle is usually 2-3 marks. A two-triangle problem, or one wrapped inside a bearing, an area or a solid, runs to 4-5. Across a series of three 80-mark papers, plan for it on both calculator papers, sometimes inside a question that is labelled as something else.
What is the difference between an angle of elevation and an angle of depression?
Both are measured from the horizontal. Elevation is the angle you look up through from a point on the ground; depression is the angle you look down through from a high point such as a cliff top. The two horizontals are parallel, so the angle of depression of a boat from the top of a cliff equals the angle of elevation of the cliff top from the boat. The common slip is measuring depression from the vertical, which gives the complement instead.

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