📐 Core Concepts
⟨ The SOH·CAH·TOA Framework ⟩
SOH
sin(θ) = Opp / Hyp
Use when you know Opposite and Hypotenuse
To find angle: θ = sin⁻¹(Opp/Hyp)
To find angle: θ = sin⁻¹(Opp/Hyp)
CAH
cos(θ) = Adj / Hyp
Use when you know Adjacent and Hypotenuse
To find angle: θ = cos⁻¹(Adj/Hyp)
To find angle: θ = cos⁻¹(Adj/Hyp)
TOA
tan(θ) = Opp / Adj
Use when you know Opposite and Adjacent
To find angle: θ = tan⁻¹(Opp/Adj)
To find angle: θ = tan⁻¹(Opp/Adj)
🎯 When to Use Which Function
Use SINE (sin⁻¹)
You have the side opposite the angle AND the hypotenuse (longest side).
Use COSINE (cos⁻¹)
You have the side adjacent (next to) the angle AND the hypotenuse.
Use TANGENT (tan⁻¹)
You have the side opposite AND the side adjacent to the angle. (No hypotenuse needed!)
💡 Worked Example — Find the missing angle x
- Identify sides: From angle x°, the side of length 4 is Opposite, the side of length 5 is the Hypotenuse. Adjacent is unknown.
- Choose function: We have Opposite and Hypotenuse → Use SIN (SOH)
- Set up equation: sin(x) = 4/5 = 0.8
- Apply inverse: x = sin⁻¹(0.8)
- Calculate: x ≈ 53.1°
📋 Practice Problems
20 QUESTIONS
Click any problem card to answer. Use the 🔊 button to hear the problem read aloud.
❌ Incorrect Answers — Review These