Sure! Let's dive into solving the problem step-by-step.
Given the equation:
[tex]\[
\sin(x) = \cos(32^\circ)
\][/tex]
we want to find the value of \( x \) such that \( 0^\circ < x < 90^\circ \).
We can use the trigonometric identity:
[tex]\[
\sin(x) = \cos(90^\circ - x)
\][/tex]
According to this identity, if \( \sin(x) = \cos(32^\circ) \), then it means:
[tex]\[
x = 90^\circ - 32^\circ
\][/tex]
Now, let's perform the subtraction:
[tex]\[
x = 90^\circ - 32^\circ = 58^\circ
\][/tex]
Therefore, the value of \( x \) is:
[tex]\[
\boxed{58^\circ}
\][/tex]
So, the answer is B. [tex]\( 58^\circ \)[/tex].
