The side measuring 6.2 is adjacent to the reference angle x. 9 is the measure of the hypotenuse. The trig ratio that relates the side adjacent to the hypotenuse is cosine. We will actually use inverse cosine because what we are looking for is an angle measure. Setting up properly, we have
. When we do the division we get cos(x) = .68888888 In order to find the angle that has a cosine ratio of .6888888, we will hit the 2nd button on our calculator and then the cos button and we will see this on our display:
and a parenthesis that is open. Enter that .688888 in and hit enter and you'll get an angle measure of 46.45 or 46.5 rounded. First choice from above.