Beyond Right Triangles

Trigonometry · Axiom Academy

Discover the limits of SOH-CAH-TOA and why we need new tools to solve any triangle SOH-CAH-TOA: The Right Triangle Champion Let's review! SOH-CAH-TOA gives us the sine, cosine, and tangent ratios for right triangles . Click on the triangle below to see these ratios in action. What If There's No Right Angle? Drag vertex C (the blue point) to change the triangle. Watch what happens when the triangle is no longer a right triangle! Hint: Try dragging point C upward or to the left to change angle B SOH-CAH-TOA requires identifying the "opposite," "adjacent," and "hypotenuse" - but these terms only make sense relative to a right angle. Without a 90° angle, we can't define which side is the hypotenuse! Most triangles in the real world aren't right triangles . We need tools that work for ANY triangle! SOH-CAH-TOA is powerful but limited to right triangles. The Law of Sines and Law of Cosines break free from that limitation, giving us the tools to solve any triangle - whether it has a right angle or not. These laws are the foundation of general trigonometry!

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