Question

The perimeter of a certain sector of a circle is equal to the length of the arc of the semicircle having the same radius express the angle of the sector in degree minutes and second

Answer 1

Answer:

Hey mate....

Step-by-step explanation:

hope it will help you...........

Answer 2

The angle of the sector in terms of degree minutes and second is  65° 27' 16".

Given:

The perimeter of the sector = the length of the arc of the semicircle.

To Find:

The angle of the sector in terms of degree, minutes, and second.

Solution:

From the figure,

The perimeter of the sector

= r + r+ l

= 2r +l

But l = rθ

⇒ The perimeter of the sector = r(2+ θ)

The perimeter of a semi-circle = π r

By given condition,

r(2+ θ) = π r

⇒ θ = π -2 radian

⇒ θ = π -2 $* \frac{180}{\pi }$ degree

$= 180 -\frac{360}{\pi }$

= 180° - 114° 32' 44"

= 65° 27' 16"

Therefore, the angle of the sector in terms of degree minutes and second is  65° 27' 16".

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