SOH-CAH-TOA Revival

Trigonometry · Axiom Academy

Discover the magic of trigonometry! Watch how the ratios in right triangles stay constant no matter the size. Every right triangle has three sides with special names. The names depend on which angle we're focusing on! Proof: Different Sizes, Same Ratios Let's compare two triangles with the same angle but different sizes. Watch the ratios! This mnemonic helps you remember which ratio is which. Click each card to see it highlighted! Architects use trig to design roofs and ramps. Surveyors measure distances across rivers. Engineers calculate forces on bridges. Astronomers measure distances to stars. GPS satellites use trig constantly! The beauty of trig is that these ratios are constants for each angle. This means once you know an angle, you can find any missing side. Or if you know two sides, you can find the angle! What you've learned here is just the beginning! These same trig functions extend to the unit circle, work for any angle (not just 0-90°), and form the foundation for waves, oscillations, and periodic phenomena throughout physics and engineering.

This is the written version of the interactive lesson above. See the full Trigonometry course.