We have a column in the Right Triangle Table labeled “.” We use this ratio so frequently that it has a name. It is called the cosine of the angle. We write “” to say “the cosine of 25 degrees.” The other columns in our table also have names: Sine is the name for the ratio “,” and tangent is the name for the ratio “.”

A scientific calculator can display these ratios for any angle. This means we can more precisely calculate unknown side lengths rather than estimating using the table. The Right Triangle Table is sometimes called a “trigonometry table” since cosine, sine, and tangent are trigonometric ratios. Here is what the table looks like with the ratios labeled with their special names:

If the length  is 7, we can find by solving the equation . So  is about 7.7 units. To solve for , we have three methods that we can use: the Pythagorean Theorem, sine, and tangent. Let’s use tangent by solving the equation . So  is about 3.3 units. We can check our answers using the Pythagorean Theorem. It should be true that . The two expressions are almost equal, which makes sense because we expect some error due to rounding.