Examples

Check if the values of the following triangles are correct

Triangle 1:

we will use the angle at the top left hand corner, 45 degrees.

using sine

thus, according to triangle 1 above,

sin 45 = opposite / hypotenuse

          = 1 / root 2

          = 0.7071 approximately

Now lets check this with your calculator. Type in sin 45 and see what you get!

sin 45 = 0.7071 

using cosine

cos 45 = adjacent / hypotenuse

           = 1 / root 2

           = 0.7071 approximately

Check again with your calculator.

cos 45 = 0.7071

and therefore the values of first triangle are correct!

Note that you only have to test one angle because they are both 45 degrees and the other angle will return the exact same result

Triangle 2:

First we will use 30 degrees.

using sine

therefore, according to the triangle 2 above,

sin 30 = opposite / hypotenuse

         = 1 / 2

Now check this with your calculator

sin 30 = 0.5

         = 1 / 2

using cosine

similarily from the triangle above

cos 30 = adjacent / hypotenuse

          = root 3 / 2

          = 0.8660

Check with your calculator:

cos 30 = 0.8660

Next we will use 60 degrees

Thus, according to the triangle 2 above,

using sine:

sin 60 = opposite /.hypotenuse

          = root 3 / 2

          = 0.8660 approximately

Check with your calculator

sin 60 = 0.8660 approximately

using cosine

cos 60 = adjacent / hypotenuse

           = 1 / 2

check with your calculator!

cos 60 = 0.5

           = 1 / 2

therefore the values of above triangles are correct!

Your turn: try these checks with tangent for both triangles!