How to Calculate Triangle Height Given Three Sides

The Organic Chemistry Tutor

This educational mathematics tutorial demonstrates how to calculate the height of a triangle when only the lengths of its three sides are known. The video guides viewers through a two-step strategy: first using Heron's Formula to determine the total area of the scalene triangle, and then substituting that area into the standard triangle area formula to solve for the unknown height. The instructor uses a specific example with side lengths of 9, 10, and 11 to make the abstract concepts concrete. A significant portion of the video focuses on algebraic skills, specifically calculating the semi-perimeter and simplifying radicals without a calculator. The instructor breaks down complex square roots by factoring numbers to find perfect squares, demonstrating an efficient mental math technique. The video concludes by setting up an algebraic equation to isolate the height variable, providing both an exact radical answer and a decimal approximation. For educators, this video serves as an excellent bridge between geometry and algebra. It reinforces key concepts like substitution, solving for variables, and properties of radicals while teaching a specific geometric application. It is particularly useful for demonstrating that height can be found for non-right triangles without using trigonometry, making it a valuable resource for high school geometry and algebra curriculums.