Note that we are given the side adjacent to the unknown angle and the hypotenuse. Therefore, to find its measure we will use the cosine ratio.
cos T = Length of leg adjacent to∠T/Length of hypotenuse
In our triangle, we have that the length of the adjacent leg to ∠T and the hypotenuse are 11 and 23.
The cosine of the angle is 1123. Now, to isolate m∠T we will use the inverse function of cos.
cos T=11/23 ⇔ m∠T=cos ^(- 1)11/23
Let's use a calculator to find the value of cos ^(- 1) 1123. First, we will set our calculator into degree mode. To do so, push MODE, select Degree instead of Radian in the third row, and push ENTER. Next, we push 2ND followed by COS, introduce the value 1123, and press ENTER.
