SOH CAH TOA is a mnemonic to help you remember the ratio of the sides that define the sine, cosine, and tangent of an acute angle in a right triangle.
Given right triangle ABC with right angle at C and sides a opposite A, b opposite B, and c the hypotenuse (opposite angle C):
`sinA=a/c,sinB=b/c` or `("side""opposite")/"hypotenuse"` (SOH -- sine is opp over hyp)
`cosA=b/c,cosB=a/c` or `("side""adjacent")/"hypotenuse"` (CAH -- cos is adj over hyp)
`tanA=a/b,tanB=b/a` or `"opposite"/"adjacent"` (TOA -- tan is opp over adj)
If you have the side lengths of the triangle you do not need a calculator to compute the sin, cos, or tan of the angles.
If you know the side lengths and are asked for the angle then you use the inverse keys. e.g. if you know that a=5 and c=13 then `sinA=5/13` so `A=sin^(-1)5/13~~22.6^@`
If you know the angle and a side (or hypotenuse) and want to know the remaining side you use the sin (or cos or tan) key: e.g. given angle A is `30^@` and c=10 then `sinA=a/13` so `sin30^@=a/13 ==>a=13sin30^@=6.5`