Question

In the diagram shown on circle A, segment CD is tangent to the circle at point D. If CD=23 and CA = 28.

Answer 1

Answer:

35°

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 $\angle D= 90\°$.

Now, we know that $CD=23$ and $CA=28$, which are leg and hypothenuse, respectively.

So, to find $m \angle C$ we just need to use trigonometric reasons, specifically, the cosine funtion, because it relates the adjacent leg and the hypothenuse.

$cos(C)=\frac{CD}{CA}=\frac{23}{28} \\C=cos^{-1}(\frac{23}{28} ) \approx 35 \°$

Therefore, the measure of angle C is 35°, approximately.