Right Triangle Trigonometry

• ·       What is soh-cah-toa and cho-sha-cao?
• ·       How do we find an unknown side length in a right triangle using trigonometric ratios?

First, we need to know what soh-cah-toa and cho-sha-cao means.

SOH- Sine(sin)= opposite over hypotenuse

CAH- Cosine(cos)= adjacent over hypotenuse

TOA- Tangent(tan)= opposite over adjacent

CHO- Cosecant(csc)= hypotenuse over opposite

SHA- Secant(sec)= hypotenuse over adjacent

CAO- Cotangent(cot)= adjacent over opposite

Notice that soh-cah-toa and cho-sha-cao are the opposites of one another.

Here's another example:

$\goldD B$start color goldD, B, end color goldD since that is the angle that is explicitly given in the diagram.

$\goldD{50^{\circ}}\,\,\,$$\purpleC{6}$$\blueD{?}$$C$$B$$A$

Note that we are given the length of the $\purpleC{\text{hypotenuse}}$start color purpleC, h, y, p, o, t, e, n, u, s, e, end color purpleC, and we are asked to find the length of the side $\blueD{\text{opposite}}$start color blueD, o, p, p, o, s, i, t, e, end color blueD angle $\goldD B$start color goldD, B, end color goldD. The trigonometric ratio that contains both of those sides is the sine. 

sin(B) = opposite/hypotenuse  define sine.

sin(50) = AC/6  substitute.

6sin(50) = AC  multiply both sides by 6.

4.60 = AC  evaluate with a calculator.