Sine of an Angle in a Right Triangle

I'll update the specification to add instructions for rendering and downloading the animation, as the user is asking how to obtain the final video file. This is added as a new note while preserving all existing content.

# Right Triangle with Sine Formula

## Overview

A right-angled triangle is drawn with its sides labeled 'Opposite', 'Adjacent', and 'Hypotenuse'. The angle \( \theta \) is highlighted, and the sine formula \( \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \) appears at the top of the screen. When the formula appears, the corresponding sides (Opposite and Hypotenuse) flash to visually connect the formula to the triangle.

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## Phases

| # | Phase Name | Duration | Description |
|---|------------|----------|-------------|
| 1 | Draw Triangle and Label | ~6s | Draw a right triangle, label the right angle, label sides 'Opposite', 'Adjacent', 'Hypotenuse'. Highlight angle \( \theta \) at the vertex opposite the Hypotenuse. |
| 2 | Show Formula and Flash | ~5s | Fade in the formula \( \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \) at the top of the screen. Simultaneously make the 'Opposite' and 'Hypotenuse' side labels or the sides themselves flash (e.g., change color briefly and return). |

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## Layout

┌─────────────────────────────────────────────┐
│ Formula Area (top) │
│ $\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$ │
├─────────────────────────────────────────────┤
│ │
│ Main Area │
│ (Right triangle with labels) │
│ │
└─────────────────────────────────────────────┘

### Area Descriptions

| Area | Content | Notes |
|------|---------|-------|
| Formula Area | The sine formula in LaTeX | Appears in phase 2; positioned near top center. |
| Main Area | Right triangle with side labels and angle \( \theta \) | Triangle drawn with standard orientation (right angle at bottom left, \( \theta \) at bottom right). Sides labeled: 'Opposite' opposite \( \theta \), 'Adjacent' adjacent to \( \theta \), 'Hypotenuse' the longest side. |

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## Notes

- The triangle should be drawn with clean, straight lines. Use a standard orientation: right angle at the bottom-left vertex, \( \theta \) at the bottom-right vertex. The side opposite \( \theta \) is vertical (labeled 'Opposite'), the side adjacent is horizontal (labeled 'Adjacent'), and the hypotenuse connects the top of the opposite side to the left end of the adjacent side.
- Label text should be clear and legible (e.g., using a sans-serif font).
- The angle \( \theta \) is highlighted with an arc and possibly the Greek letter theta.
- The flash effect for the sides in phase 2 should be brief (e.g., turn yellow or white for 0.5s and then return to original color). It can apply to the side lines themselves, the labels, or both — visually connecting the formula's numerator and denominator.
- Keep the animation concise: total duration ~11 seconds, well under 30 seconds.
- **How to download / render the animation:**  
  To obtain the final video file, the user should run the Manim code for this scene. Typically this is done from the command line using a command such as:  
  `manim -pql script.py SceneName`  
  where `script.py` is the file containing the animation code. The `-p` flag plays the output after rendering; `-ql` or `-qh` selects low or high quality. The rendered video file (e.g., MP4) is saved automatically to the `media/` folder (e.g., `media/videos/script/480p15/SceneName.mp4`). For specific download instructions, the user should consult the Manim documentation or the platform where the code is being executed (e.g., Jupyter, online colab, or local environment).