Activity #3:

Read the following.

It was discovered that if two right triangles of different sizes but having the same angular measures were compared, the ratios of their sides in reference to the degree measured angle would always be the same.

Looking at these right triangles, you can easily see that they each have a 30⁰ angle and the sides of each triangle are given. For each triangle, if you took the measurement of the side opposite the 30⁰ angle over the hypotenuse of the triangle, you would find the ratio, calculated out to the nearest ten-thousandths place, to be .5000. Over thousands of years, mathematicians discovered this ratio and gave it a name - it's called the sine ratio.

sin 30⁰ = 3 = .5000 and sin 30⁰ = 9 = .5000
                6                                        18

Further study resulted in the labeling of 2 more ratios. The first is called the cosine ratio. It is calculated by using the length of the side adjacent to the reference angle placed over the length of the hypotenuse.

                    cos 30⁰ = 5.1962 = .8660 and cos 30⁰ = 15.5885 = .8660
                                          6                                                     18

The third ratio discovered was labeled the tangent ratio. It is calculated by using the length of the side opposite the reference angle placed over the length of the side adjacent.

tan 30⁰ = . 3       .  = .5774      and tan 30⁰ = . 9     .=       .5774
                5.1962                                             15.885
    

An easy nonsense phrase to help remember the functions is

SOH CAH TOA.

Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, and Tangent is Opposite over Adjacent.