Certainly! Let's solve the given problem step-by-step.
We know from trigonometric identities that the sine of an angle is equal to the cosine of its complementary angle. Specifically:
[tex]\[ \sin(36^\circ) = \cos(\theta) \][/tex]
The equation above tells us that the angle [tex]\(\theta\)[/tex] is complementary to 36 degrees. In trigonometry, two angles are complementary if their sum is 90 degrees.
Therefore, we can write the relationship between the angles as:
[tex]\[ \theta = 90^\circ - 36^\circ \][/tex]
Now let's calculate:
[tex]\[ \theta = 90^\circ - 36^\circ \][/tex]
[tex]\[ \theta = 54^\circ \][/tex]
So, the measure of [tex]\(\theta\)[/tex] is 54 degrees.
To summarize, [tex]\(\theta = 54^\circ\)[/tex].
