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22 July, 23:22

If UC=5, and the area of the sector of the circle enclosed by the central angle subtended by UN⌢ is 6.54 in2, what is m∠UCN? Round to nearest degree

A:30

B: 150

C: 27

D: 330

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Answers (1)
  1. 22 July, 23:35
    0
    m∠UCN = 30° to the nearest degree ⇒ answer (A)

    Step-by-step explanation:

    * Lets talk about the area of the sector

    - Any sector of a circle formed by 2 radii and an arc

    - The central angle formed from the two radii is subtended by this arc

    - The area of this sector = (1/2) r²Ф, where r is the length of the radius

    and Ф is the central angle with radiant measure

    * Lets revise how to change the measure of the angle from radiant to

    degree or from degree to radiant

    ⇒Ф° * π/180 = Ф radiant

    ⇒Ф radiant * 180/π = Ф degree

    * Now lets solve the problem

    - UC is the radius of the circle C

    - Un is an arc subtended to the central angle UCN

    ∵ UC = 5 ⇒ r = 5 inches

    ∵ The area of the sector enclosed by the central angle UCN (Ф)

    and the two radii CU and CN is 6.54 inches²

    ∵ Area the sector = (1/2) r²Ф

    ∴ (1/2) (5) ²Ф = 6.54

    ∴ 25/2 Ф = 6.54 ⇒ divide the both sides by 25/2

    ∴ Ф = 6.54 / (25/2) = 0.5232 radiant

    * Lets change the measure from radiant to degree

    ∴ Ф° = 0.5232 * (180/π) = 29.977 ≅ 30° to the nearest degree

    * The measure of the central angle UCN is 30°
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