Answer:
<h2>35°</h2>
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 .
Now, we know that and , which are leg and hypothenuse, respectively.
So, to find we just need to use trigonometric reasons, specifically, the cosine funtion, because it relates the adjacent leg and the hypothenuse.
Therefore, the measure of angle C is 35°, approximately.