Question

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?

Answer 1

(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°.

Answer 2

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°