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There is a balcony that forms part of a circle around a stage, and they need to put up a safety railing. How long of a railing do they need if the radius of the circle is 40 feet, and the arc takes up 45°? Use 3.14 for pi.

Sagot :

olayemiolakunle65

A sector is a part of a circle that is formed by two radii, and an arc. So that the length of the safety railing required is 31.4 feet.

A sector is a part of a circle that is formed by two radii, and an arc, thus forming a central angle.

Thus the required length of safety railing can be considered as the arc of the sector.

So that;

length of an arc = (θ / [tex]360^{o}[/tex]) * 2[tex]\pi[/tex]r

where θ is the measure of the central angle of the sector, and r is the radius of the sector.

From the given question, θ = 45°, and r = 40 feet.

So that,

length of the safety railing = (45° / [tex]360^{o}[/tex]) * 2 * 3.14 * 40

                                 = 0.125 * 2* 3.14* 40

length of safety railing = 31.4

Therefore, the length of the safety railing required is 31.4 feet.

For more clarifications on the length of an arc, visit: https://brainly.com/question/2005046

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