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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 CD23 and CA28 then which one of the following is closest to mC class=

Respuesta :

Answer:

m∠C = 35°

Step-by-step 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°

xero099

Answer:

(4) 35°.

Step-by-step explanation:

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

[tex]\theta = \cos^{-1}\left(\frac{CD}{CA} \right)[/tex]

[tex]\theta = \cos^{-1}\left(\frac{23}{28} \right)[/tex]

[tex]\theta \approx 34.772^{\circ}[/tex]

The right answer is (4) 35°.

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