Note that we are given the opposite side to the unknown angle and the hypotenuse. Therefore, to find its measure we will use the sine ratio.
sin A = Length of leg opposite to∠ A/Length of hypotenuse
In our triangle, we have that the length of the leg opposite to ∠ A and the hypotenuse are 22 and 35.
The sine of the angle is 2235. Now, to isolate m∠ A we will use the inverse function of sin.
sin A=22/35 ⇔ m∠ A=sin ^(- 1)22/35
Let's use a calculator to find the value of sin ^(- 1) 2235. 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 2235, and press ENTER.
The angle is about 38.9^(∘), which corresponds to option B.
