Solving The 30-60-90 Triangle Ratios

This animation shows a 30°-60°-90° triangle with the side opposite the 30° angle given as 4 units. It visually builds the fixed side ratio 1:√3:2, highlighting how each side relates to the hypotenuse. Step by step, it multiplies the short leg by √3 to reveal the side opposite the 60° angle, giving 4√3. Useful for students learning special right triangles and preparing for trigonometry or geometry exams.

Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy

The prompt that made it

In a 30°–60°–90° triangle, the side opposite the 30° angle measures 4 units. What is the length of the side opposite the 60° angle? Color Scheme: #17271F #101B16 #5E6961 #D6EE59 #F5F6F1 #D9DFD3 Use lighter color for background. Audience: 13-18

Make your own version

Make the next one in this series

• Derive the 1:√3:2 ratio by splitting an equilateral triangle in half
• Show the 45-45-90 triangle ratio and compare it side by side with 30-60-90
• Apply the 30-60-90 ratio to find a building's height using shadow length