SOH-CAH-TOA Applications — Quick Reference Cheatsheet
A focused companion to the main SOH-CAH-TOA Applications topic page on ACT Math.
ACT Math Trigonometry One-page reference
This is a one-page reference for SOH-CAH-TOA Applications on the ACT math section. Apply trig ratios to solve problems involving angles of elevation and depression. Use it as a printable cheatsheet before test day, or as a refresher right before you attempt the worked questions on the main SOH-CAH-TOA Applications topic page.
What this topic is
A SOH-CAH-TOA Applications question tests sine, cosine, tangent, identities, and the laws of sines and cosines. SOH-CAH-TOA must be automatic.
Core formulas you must memorise
- sin = opp/hyp ; cos = adj/hyp ; tan = opp/adj
- sin²θ + cos²θ = 1
- Law of sines: a/sin A = b/sin B = c/sin C
- Law of cosines: c² = a² + b² − 2ab cos C
- Common angles: 30° → ½, 45° → √2/2, 60° → √3/2
If any of these formulas are not yet automatic, drill them via the Trigonometry formula sheet. Memorisation is fastest when you write each formula out by hand five times in a row, then quiz yourself the next morning.
How to spot this question type on the test
ACT questions on SOH-CAH-TOA Applications typically present in one of three ways: as a pure symbolic problem ("solve for x"), wrapped in a word problem (a real-world scenario you must translate), or hidden inside a longer multi-step question where SOH-CAH-TOA Applications is just the first or last step. Train yourself to recognise the signature — a particular word, equation form, or diagram — and you will halve your reading time.
The 30-second decision
Check whether the calculator is in degrees or radians BEFORE punching in any numbers.
If you have 60 seconds before the question
Glance at the answer choices first. If they are widely spaced, estimate; if they are close, you must be exact. Sketch any diagram involved. Identify which of the formulas above applies. Then attempt — and if you cannot finish in 90 seconds, mark and move on. There is no penalty for guessing on either the SAT or the ACT, so always bubble in.
Drill set
Re-attempt the six worked SOH-CAH-TOA Applications questions with this cheatsheet open. Then close it and re-attempt them from memory. If you can solve all six without peeking, this topic is locked in.
Related study material
For broader test-prep tactics, see our SOH-CAH-TOA Applications strategy guide. For category-wide context, browse all Trigonometry topics. For score-targeted study plans, see the score-band guides.