Interactive Workbook — SOH·CAH·TOA
MISSING
ANGLES
Learn when to apply sine, cosine, and tangent — then prove it with 20 progressively challenging problems.
01 · The Three Sides
Naming the Sides
Fix angle θ in a right triangle — every side instantly gets a role.
Opposite — across from θ ·
Adjacent — beside θ (not the hypotenuse) ·
Hypotenuse — longest side, opposite 90°
03 · Worked Examples
SOH — sin⁻¹
Example A | Opp = 9, Hyp = 15
1Given: Opp = 9, Hyp = 15 → O & H → SOH
2
3
4
CAH — cos⁻¹
Example B | Adj = 11, Hyp = 20
1Given: Adj = 11, Hyp = 20 → A & H → CAH
2
3
4
TOA — tan⁻¹
Example C | Opp = 7, Adj = 5
1Given: Opp = 7, Adj = 5 → no hyp → TOA
2
3
4
02 · SOH CAH TOA
The Three Ratios
Each ratio links angle θ to exactly two sides:
Decision Table
| Given | Find | Function | Why |
|---|
| Opp + Hyp |
x° | sin⁻¹ |
SOH → O & H |
| Adj + Hyp |
x° | cos⁻¹ |
CAH → A & H |
| Opp + Adj |
x° | tan⁻¹ |
TOA → no Hyp |
Inverse key: press 2nd or SHIFT + sin/cos/tan on your
calculator to solve for the angle. Written sin⁻¹, cos⁻¹, tan⁻¹.
READY TO
PRACTICE?
Final Score
—%
Complete the problems and click Results.