So far in this unit we've looked at what the trig functions are, but we begin to understand the real power of these functions when we pull our calculator into play. Just for review, here are our trig functions again for right triangle ABC, with right angle at C (as shown in the diagram below):

sin A = a/c
cos A = b/c
tan A = a/b


Using Your Calculator
Your calculator will provide you with the trig functions for any angle you enter. For example, if you press the SIN button, followed by the number 30, then press ENTER, the calculator will display: 0.5.

This means that sin 30 = 0.5.

Can you find the cos 30 the same way? You should get approximately 0.866.

How is this useful to us? Take a look:

Sample #1
If measure of angle A is 25 degrees, and c = 20, find the length of a.

Solution
sin 25 = a / 20

Now pull out your calculator and enter sin 25. You should see the following result: 0.3420. Therefore:

0.3420 = a/20

Now just multiply both sides by 20, and you have:

a = 6.84

Sample #2
If B = 40 degrees, and b = 10, find a.

Solution
tan B = b / a
tan 40 = 10 / a
.8391 = 10 / a
a = 11.92

Sample #3
If A = 45 degrees, and a = 3, find c.

Solution
sin A = a / c
sin 45 = 3 / c
0.7071 = 3 / c
c = 4.24