Section 01
Right Triangles & Their Sides
Naming the Three Sides — Based on Angle θ
In a right triangle, once you identify angle θ (theta), the names of all three sides are determined.
Key: The side across from θ → Opposite; the side next to θ (not the hypotenuse) → Adjacent; always the longest side → Hypotenuse.
SOH — CAH — TOA
The golden mnemonic for all three trig ratios:
When Do You Use Each Function?
| Given Sides |
Find |
Function |
Memory Aid |
| Opposite + Hypotenuse |
Angle x |
sin⁻¹ |
SOH → O & H → use sin |
| Adjacent + Hypotenuse |
Angle x |
cos⁻¹ |
CAH → A & H → use cos |
| Opposite + Adjacent |
Angle x |
tan⁻¹ |
TOA → O & A → use tan |
Inverse Trig Functions: To find an angle, press 2nd or SHIFT + sin/cos/tan on your calculator.
Worked Examples
Example A — sin⁻¹ | Opposite = 9, Hypotenuse = 15
📐 Example A — SOH
1Identify given sides: Opposite = 9, Hypotenuse = 15 → Use SOH
2
3
4
Example B — cos⁻¹ | Adjacent = 11, Hypotenuse = 20
📐 Example B — CAH
1Identify given sides: Adjacent = 11, Hypotenuse = 20 → Use CAH
2
3
4
Example C — tan⁻¹ | Opposite = 7, Adjacent = 5
📐 Example C — TOA
1Identify given sides: Opposite = 7, Adjacent = 5 → Use TOA
2
3
4