A mnemonic for the relationships between the sine, cosine and tangent functions to the lengths of the "opposite", "adjacent", and "hypoteneuse" sides of a right triangle. (The way it was told to me, "Sohcahtoa" was the name of a mathematician Indian chief.)

SOH: Sine = Opposite / Hypoteneuse
CAH: Cosine = Adjacent / Hypoteneuse
TOA: Tangent = Opposite / Adjacent

Okay, so imagine that there are two squaws, each of them with their respective sons. There is a third squaw, Sohcahtoa, without a son. Each is sitting on an animal hide.

The son of the squaw on the deer hide weighs 130lbs. The son of the squaw on the elk hide weighs 120lbs. Sohcahtoa, sitting on a hippopotamus hide, weighs 250lbs.

So the squaw on the hippopotamus is equal to the sons of the squaws on the other two hides.

There you go. The Pythagorean theorem, done with Sohcahtoa.

PS: I always learned it "Oscar Had A Heap Of Apples, Sam Carried Them." The decoding is the same, but in a more nonsensical order. The first two letters (O and H) match the S in "Sam", for Sine = Opposite over Hypotenuse.

Source is my faulty memory of my 9th grade geometry book.

A slightly altered version of mdwyer's tale of the squaw of Sohcahtoa.

A tribe of Native Americans generally referred to their womenfolk by the animal hide with which they made their blankets. Thus, one woman might be known as Squaw of Buffalo Hide, while another may be known as Squaw of Deer Hide. This tribe had a particularly large and strong woman with a unique animal hide for her blanket. She was known as Squaw of Hippopotamus Hide, and she was as strong and powerful as the animal from which she made her blanket.

Each year, she entered the tribal wrestling contest, and easily defeated all challengers, male or female. As the men of the tribe admired her strength and power, this made many of the other women of the tribe quite jealous. So one year, two of them decided to enter their sons into the tournament as a team. The Chief of the tribe agreed.

As luck would have it, the team met the squaw in the final. As the match began, it became clear that the squaw had finally met her match. The two sons wrestled and struggled as much as they could, but they could not bring her down. Likewise, the squaw did not give in, and tried unsuccessfully to become champion again. Finally, the Chief intervened and declared that, in the interests of health and safety, the match was to be terminated and the winner would be decided by himself. With that, he retired to his teepee.

For days, the Chief could not pick a winner. While the two young men had matched the squaw's power, the Chief found it difficult force the squaw to relinquish her championship. After all, it had taken two men to finally provide her with a decent challenge. What to do? Then the Chief remembered Pythagoras, a visitor from Greece who was staying with the tribe for a while. Pythagoras sat down in the Chief's teepee, thinking, and after a few moments, it came to him. He exited the teepee, called the tribe to assembly, and announced his decision:

"The Squaw of the Hippopotamus is equal to the sons of the squaws of the other two hides."

Source: Mensa Maths Wizard for Kids (1998)

By the way, another way to remember SOHCAHTOA would be:

  • Some
  • Old
  • Hairy (or heavy)
  • Cows
  • Are
  • Hairier (or heavier)
  • Than
  • Others
  • Are

Then again, you can also just say to yourself "Soccer-toe-ah."

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