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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