Sine Ratio
Opposite over hypotenuse.
Key idea
Opposite over hypotenuse.
In depth
sin θ = opposite / hypotenuse. All right triangles with the same acute angle are similar, so this ratio depends only on the angle, not on the size. That is what makes it a function of θ.
Worked example
In a 3-4-5 triangle, sin of the angle opposite 3 is 3/5 = 0.6.
Formula
Real-world uses
- Finding the height of a kite or tree from its angle of elevation and string length
Common mistake
Using the adjacent side. That is cosine.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Sine Ratio?
Opposite over hypotenuse. It is a topic at the intermediate level in Trigonometry.
What is the formula for Sine Ratio?
The key formula is sinθ = opp/hyp.
Where is Sine Ratio used in real life?
Real-world examples: Finding the height of a kite or tree from its angle of elevation and string length.
What should I learn before Sine Ratio?
Make sure you are comfortable with Right Triangle Terminology, the previous topic in Trigonometry.
What is a common mistake with Sine Ratio?
Using the adjacent side. That is cosine.
How can I practise Sine Ratio?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Sine Ratio?
Move on to Cosine Ratio next.
Related intermediate topics in Trigonometry
- Radians – Angle measured by arc length on a unit circle; 2π rad = 360°.
- Converting Degrees and Radians – Multiply by π/180 or 180/π.
- Cosine Ratio – Adjacent over hypotenuse.
- Tangent Ratio – Opposite over adjacent.
- Reciprocal Trig Functions – Cosecant, secant and cotangent.
- Solving Right Triangles – Find all sides and angles using ratios and the Pythagorean theorem.