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The Mnemonic[edit | edit source]

Soh-Cah-Toa is a mnemonic for remembering how to use sines, cosines, and tangents to compute lengths in right angle triangles.

Trigonometric definitions[edit | edit source]

right triangle This triangle has sides a and b. The angle between them, C, is a right angle. The third side, c, is the hypotenuse. Side a is opposite angle A, and side b is adjacent to angle A.

Applying the definitions of the functions, we have:

or opposite side over hypotenuse
or adjacent side over hypotenuse
or opposite side over adjacent side

This can be memorized using the mnemonic 'SOH-CAH-TOA' (sin = opposite over hypothenuse, cosine = adjacent over hypotenuse, tangent = opposite over adjacent).

Video Link[edit | edit source]

These links from the Khan Academy are useful for this topic.

Exercises: (Draw a diagram!)[edit | edit source]

Exercise: Find sin cos and tan
  • A right triangle has side a = 3, b = 4, and c = 5.
  • Calculate the following:
Exercise: Find a side
  • A different right triangle has side and .
  • Calculate side a.