01 Key Concepts
Right Triangle Sides
Relative to a chosen angle: the hypotenuse (longest side, opposite the right angle), the opposite side (across from the angle), and the adjacent side (next to the angle, not the hypotenuse).
Sine (sin)
sin(angle) = opposite / hypotenuse.
Cosine (cos)
cos(angle) = adjacent / hypotenuse.
Tangent (tan)
tan(angle) = opposite / adjacent, which also equals sin(angle)/cos(angle).
SOH-CAH-TOA
A memory aid: Sine=Opposite/Hypotenuse, Cosine=Adjacent/Hypotenuse, Tangent=Opposite/Adjacent.
Common Angle Values
sin(30°)=0.5, cos(30°)=sqrt(3)/2, sin(45°)=cos(45°)=sqrt(2)/2, sin(60°)=sqrt(3)/2, cos(60°)=0.5.
02 Key Formulas
- sin(A) = opposite/hypotenuse
- cos(A) = adjacent/hypotenuse
- tan(A) = opposite/adjacent
03 Solved Examples
Example 1 A right triangle has opposite side 3, hypotenuse 5. Find sin(A).
- Apply the formula: sin(A) = opposite/hypotenuse = 3/5.
Answer: sin(A) = 0.6
Example 2 A right triangle has adjacent side 4, hypotenuse 5. Find cos(A).
- Apply the formula: cos(A) = adjacent/hypotenuse = 4/5.
Answer: cos(A) = 0.8
Example 3 A right triangle has opposite side 3, adjacent side 4. Find tan(A).
- Apply the formula: tan(A) = opposite/adjacent = 3/4.
Answer: tan(A) = 0.75
04 Practice Questions
1A triangle has opposite 6, hypotenuse 10. Find sin(A).
0.6
2A triangle has adjacent 8, hypotenuse 10. Find cos(A).
0.8
3A triangle has opposite 6, adjacent 8. Find tan(A).
0.75
4What does SOH stand for?
Sine = Opposite/Hypotenuse
5Find sin(30°).
0.5
📄 Trigonometric Ratios — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.