SOHCAHTOA (trigonometry) – GCSE Maths

Foundation and Higher · Grade 5 · Calculator

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Trigonometry at this grade is three ratios that compare two sides of a right-angled triangle. From the acute angle you are working with, the opposite side is across the triangle, the adjacent side is the other side that touches the angle, and the hypotenuse is always opposite the right angle. $\sin \theta =\frac{\text{opp}}{\text{hyp}}$, $\cos \theta =\frac{\text{adj}}{\text{hyp}}$, $\tan \theta =\frac{\text{opp}}{\text{adj}}$.

The whole skill is choosing the ratio that uses the two sides in the question. Tick the side you know and the side you want; the ratio that mentions exactly those two is the one to write. If the unknown is on top of the fraction, multiply. If the unknown is on the bottom, divide. To find an angle, write the ratio and take the inverse: ${\sin }^{-1}$, ${\cos }^{-1}$ or ${\tan }^{-1}$.

Your calculator must be in degrees. A 3-second check: $\sin 30^{\circ }$ should be $0.5$. Angles of elevation (looking up from the horizontal) and depression (looking down from the horizontal) are just this same triangle with a story attached.

Objectives

• Write sine as opposite over hypotenuse.
• Write cosine and tangent as the matching ratios.
• Find an opposite side from 30 degrees or 45 degrees.

Key points

• Label H, O and A from the angle in the question — not from the other acute angle.
• Choose SOH, CAH or TOA from the two sides involved.
• Find a missing side, including when the unknown sits on the bottom of the fraction.
• Find a missing angle with ${\sin }^{-1}$, ${\cos }^{-1}$ or ${\tan }^{-1}$.

Worked examples

Questions and answers

GCSE Maths sohcahtoa (trigonometry) questions and answers. Try each one, then open the answer. Easy questions come first.

Common mistakes

Most lost marks on this topic are one slip.

1. Inverting the trig fraction

   Always check: sin = Opp/Hyp, cos = Adj/Hyp, tan = Opp/Adj

2. Using adjacent instead of hypotenuse for sine

   Hypotenuse is always the side opposite the right angle

3. Assuming sin 45 is 1/2

   sin 30 is 1/2; sin 45 is √2/2

Exam tips

• A calculator is useful here. Show the calculation you typed, not only the final line.
• If the question says “show that”, the result is given. The marks are for the steps that reach it.
• The method is the same on AQA-style and Edexcel-style papers.
• Write the substituted ratio ($\sin 28^{\circ }=\frac{x}{14.6}$) before pressing any buttons. That line is the method mark.
• Store the unrounded angle and reuse it in part (b).

Printable worksheet

The same questions are in a PDF you can print. Answers start on a later page.

Download worksheet (PDF)

Or use Print in your browser. Answers under each question are included when you print.

Questions students ask

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More on SOHCAHTOA (trigonometry)

• SOHCAHTOA (trigonometry) worked examples and method
  The method in order, key facts and the full lesson explanation
• SOHCAHTOA (trigonometry) practice questions
  A second set of questions with answers, plus quick checks

AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Last updated 9 November 2026.