Note that we are given the opposite side to the unknown angle and a hypotenuse. Therefore, to find its measure we will use the sine ratio.
sin x = Length of leg opposite tox/Length of hypotenuse
In our triangle, we have that the length of the opposite leg to x and hypotenuse are 4 and 7.
The sine of the angle is 47. Now, to isolate x we will use the inverse function of sin.
sin x=4/7 ⇔ x=sin ^(- 1)4/7
Let's use a calculator to find the value of sin ^(- 1) 47. 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 SIN, introduce the value 47, and press ENTER.
