113k views
4 votes
In the diagram shown on circle A, segment CD is tangent to the circle at point D. If CD=23 and CA=28, then which one of the following is closest to m∠C?

In the diagram shown on circle A, segment CD is tangent to the circle at point D. If-example-1

2 Answers

6 votes

Answer:

(4) 35°.

Explanation:

The value of the angle is given by the following inverse trigonometric function:


\theta = \cos^(-1)\left((CD)/(CA) \right)


\theta = \cos^(-1)\left((23)/(28) \right)


\theta \approx 34.772^(\circ)

The right answer is (4) 35°.

User Foxlab
by
8.6k points
3 votes

Answer:

m∠C = 35°

Explanation:

Data

  • CD = 23
  • CA = 28

From the figure, it can be seen that a right triangle is formed where CA is the hypotenuse and CD is one of the legs.

From definition:

cos(C) = adjacent/hypotenuse

cos(C) = CD/CA

cos(C) = 23/28

m∠C = arccos(23/28)

m∠C = 35°

User Leetbacoon
by
7.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories