Sine Ratio

Understanding the Sine Ratio
The sine ratio is one of the three primary trigonometric ratios (along with cosine and tangent) used to relate angles to side lengths in right-angled triangles. It is essential for solving problems in geometry, physics, engineering, and more.

The following diagram shows the sine ratio and examples of using the ratio to find missing side lengths. Scroll down the page for more examples and solutions for the sine ratio.

Trigonometry Worksheets
Practice your skills with the following worksheets:
Printable & Online Trigonometry Worksheets

1. Definition of the Sine Ratio
   For a given angle θ in a right-angled triangle:
   \( sin(θ) = \frac{Opposite}{Hypotenuse} \)
   where
   Opposite is the side directly across from angle θ.
   Hypotenuse is the side opposite the right angle.

2. Identifying Sides:
   When working with a right-angled triangle and a specific acute angle, it’s crucial to correctly identify the three sides:
   Hypotenuse: Always the longest side, opposite the 90-degree angle.
   Opposite: The side that is directly across from the angle you are considering.
   Adjacent: The side that is next to the angle you are considering (and is not the hypotenuse).
   

3. How to Use the Sine Ratio:
   The sine ratio is used to find:
   The length of the opposite side if you know the angle and the hypotenuse.
   The length of the hypotenuse if you know the angle and the length of the opposite side.
   The measure of the angle if you know the lengths of the opposite side and the hypotenuse. Use sin⁻¹ to find missing angles.

4. SOH CAH TOA:
   A helpful mnemonic to remember the basic trigonometric ratios is SOH CAH TOA:
   SOH: Sine = Opposite / Hypotenuse
   CAH: Cosine = Adjacent / Hypotenuse
   TOA: Tangent = Opposite / Adjacent
   For learning about the sine ratio, just focus on the SOH part.

The Sine Ratio - Basic Trig GCSE/High School Math
Where do sine numbers come from? And how do we find the sine of an angle?
What is the sine ratio? Plus an example to illustrate

• Show Step-by-step Solutions

Trigonometry SOHCAHTOA GCSE Higher Maths

• Show Step-by-step Solutions

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