SOH CAH TOA: Which Trig Ratio to Use | Maths

Sin, cos or tan? Picking the right ratio is where most trigonometry mistakes happen. In this letsBug Maths lesson we see why the ratios work, label opposite / adjacent / hypotenuse properly, and use a 3-step method to choose SOH, CAH or TOA every time. Then we find sides, angles, the steepest a wheelchair ramp is allowed to be, and the height of a building from the ground. Full written guide: https://blog.letsbug.in/2026/10/soh-c... For anyone who wants to really understand it: students from Class 8 to 12, GCSE, IGCSE and ICSE, parents and curious adults. Syllabus match: Class 10 & GCSE Maths. Key idea In a right-angled triangle, label the sides FROM THE ANGLE you are using: hypotenuse = longest side, opposite the right angle; opposite = across from the angle; adjacent = next to the angle. sin = O/H, cos = A/H, tan = O/A (SOH CAH TOA) 3 steps: 1) label O, A, H 2) tick the side you know and the side you want 3) the two ticks pick the ratio. Unknown on top: multiply. Unknown on the bottom: divide. Angle: use the inverse (shift + sin / cos / tan). Check your calculator is in degrees: sin 30 must give 0.5. Practice 1) A kite string 25 m long makes 52° with the ground. How high is the kite? (3 s.f.) Answer: sin 52 = h/25, h = 25 sin 52 = 19.7 m. 2) A ramp rises 0.6 m over 7.5 m along the ground. Find its angle. Is it within 1:12? Answer: tan θ = 0.6/7.5 = 0.08, θ = 4.6°. 0.08 is less than 1/12, so yes. 3) A 4.2 m ladder's foot is 1.1 m from a wall. Find the angle with the ground (1 d.p.). Answer: cos θ = 1.1/4.2, θ = 74.8°. Study material & sources OpenStax Precalculus 2e, 5.4 Right Triangle Trigonometry (SOH CAH TOA, height of a tree from an angle of elevation): https://openstax.org/books/precalculu... (verified) Trigonometric functions (why the ratios depend only on the angle; inverse notation), Wikipedia: https://en.wikipedia.org/wiki/Trigono... (verified) Mnemonics in trigonometry (SOH-CAH-TOA), Wikipedia: https://en.wikipedia.org/wiki/Mnemoni... (verified) Grade (slope): rise over run and the angle, Wikipedia: https://en.wikipedia.org/wiki/Grade_(...) (verified) Radian (degrees vs radians), Wikipedia: https://en.wikipedia.org/wiki/Radian (verified) Theodolite (the surveyor's angle instrument), Wikipedia: https://en.wikipedia.org/wiki/Theodolite (verified) 2010 ADA Standards for Accessible Design, 405.2 ramp slope 1:12 (US Access Board): https://www.access-board.gov/files/ad... (verified) Chapters 0:00 The wheelchair ramp problem 0:38 Why trig ratios work (same angle, same ratios) 1:13 Labelling opposite, adjacent and hypotenuse 1:55 SOH CAH TOA 2:33 Which ratio? A 3-step method 3:01 Finding a side: the roof 3:46 Unknown on the bottom: the classic mistake 4:49 Finding an angle: the inverse 5:21 Calculator check: degrees, not radians 5:44 Back to the ramp 6:19 Pause and try: how tall is the building? 6:59 Two last checks 7:25 Recap and next time #SOHCAHTOA #Trigonometry #SinCosTan #RightAngledTriangle #letsBug #AngleOfElevation #StudyWithMe Connect with me - Instagram 👇   / aniketsingh6967   GitHub 👇 https://github.com/Aniket-git-hub/ LinkedIn 👇 www.linkedin.com/in/aniket-singh-80371b201 Blog 👇 https://blog.letsbug.in Thanks for watching 😀 Like share and subscribe