Soh-Cah-Toa is a mnemonic for remembering how to use sines cosines and tangents to compute lengths in right angle triangles.
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).
These links from the Khan Academy are useful for this topic.
Exercises: (Draw a diagram!)
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.