Solving 30-60-90 Special Right Triangles

The Organic Chemistry Tutor

This instructional video provides a comprehensive tutorial on understanding and solving 30-60-90 special right triangles, a fundamental concept in high school geometry and trigonometry. The narrator utilizes a digital whiteboard to visually demonstrate the invariant ratios between the sides of these triangles: the side opposite 30° is x, the side opposite 60° is x√3, and the hypotenuse is 2x. The video breaks down the logic into a set of simple rules involving multiplication and division to transition between side lengths depending on which side is known. The content progresses from basic examples to more complex problems, covering various scenarios such as starting with the short leg, the long leg, or the hypotenuse. Crucially, it addresses algebraic skills often required in these problems, such as working with radicals and rationalizing the denominator. The video concludes with a challenging application problem typical of standardized tests like the SAT, integrating the 30-60-90 triangle rules with circle geometry to find the area of a shaded region. For educators, this video serves as an excellent resource for scaffolding lessons on special right triangles. It offers clear, step-by-step procedural fluency practice while also touching on conceptual understanding of geometric relationships. The final problem provides a perfect extension for advanced students, demonstrating how basic geometric theorems apply to composite shapes and area calculations, making it valuable for both core curriculum instruction and test preparation.