Answer:
Step-by-step explanation:
The diagram is shown in the image attached.
A tangent is a line that intercepts at one unique point. When we have a tangent about a circle, an important results is that the tangent is perpendicular to the radius, because a radius can be seen as perpendicular to any point of the circle.
That means, the triangle formed ADC is a right triangle, because [tex]\angle D= 90\°[/tex].
Now, we know that [tex]CD=23[/tex] and [tex]CA=28[/tex], which are leg and hypothenuse, respectively.
So, to find [tex]m \angle C[/tex] we just need to use trigonometric reasons, specifically, the cosine funtion, because it relates the adjacent leg and the hypothenuse.
[tex]cos(C)=\frac{CD}{CA}=\frac{23}{28} \\C=cos^{-1}(\frac{23}{28} ) \approx 35 \°[/tex]
Therefore, the measure of angle C is 35°, approximately.
