Tritrig

In a right-angled triangle the hypotenuse is opposite to the right-angle..

Side a is opposite to angle A and adjacent to angle B.

Side b is opposite to angle B and adjacent to angle A.

If an angle is made bigger, then the side opposite must become longer

So there is a direct relationship between the size of an angle and the length of its opposite side and the Sin, Cos and Tan ratios are used to works out angles from the lengths of sides, or the lengths of sides from angles.

As you can see in the animation, as angle A changes then so does the length of the opposite side. The side adjacent to A stays 10cm. The ratio of thes two sides (quite simply the opposite side divided by the adjacent side) is the tangent of the angle which is found using a calculator.

For example, when the opposite side is 3.6, then 3.6 ÷ 10 = 0.36 and putting SHIFT tan 0.36 = into the calculator gives 20° to the nearest degree.

Some calculators have INV or 2ndF instead of SHIFT

And make sure that degree mode is used, not RAD or GRA

This is written down as

You will also have noticed in the animation that as the angle changes, then so does the length of the hypotenuse. The sine and cosine ratios use the hypotenuse in a similar method to the tangent.