A sector Whos radius is 10 feet, has an area of 200pi/9 ft squared. What are the measures of the central and inscribed angels for this secto

Question

A sector Whos radius is 10 feet, has an area of 200pi/9 ft squared. What are the measures of the central and inscribed angels for this sector?

in progress 0
Adeline 1 week 2021-11-19T14:29:14+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-11-19T14:30:16+00:00

    Answer:

    \theta=\dfrac{4\pi}{9}
    .

    Step-by-step explanation:

    Given information:

    Radius = 10 feet

    Area = \frac{200\pi}{9} sq. ft.        …(i)

    We need to find the measures of the central and inscribed angels for this sector.

    The area of a sector is

    A=\dfrac{1}{2}r^2\theta

    where, r is radius and \theta is central angle in radian.

    Substitute r = 10 in the above formula.

    A=\dfrac{1}{2}(10)^2\theta

    A=50\theta      …(ii)

    From (i) and (ii), we get

    50 \theta=\dfrac{200\pi}{9}

    \theta=\dfrac{200\pi}{9\times 50}

    \theta=\dfrac{4\pi}{9}

    Therefore, the measure of central angle is \dfrac{4\pi}{9}.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )