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Determine the length of a 45.0° arc for a circle with a diameter of 5.00 meters. Express the answer to 2 decimal places and use [tex] \pi = 3.14 [/tex].

A) 1.57 meters
B) 2.36 meters
C) 3.14 meters
D) 3.93 meters

Answer :

Final answer:

To find the length of an arc in a circle, use the formula: arc length = radius x angle in radians. After converting the given 45° to radians (which approximate 0.785398163 radians) and finding the radius of the circle (2.5m), we find that the length of the arc in this case is approximately 1.96 meters. The closest answer to this, up to the given precision, is 2.36 meters.

Explanation:

The question asks to determine the length of a 45.0° arc for a circle with a diameter of 5.00 meters. In order to solve this, we need to know the relationship between the arc length, radius and the angle subtended by the arc at the center of the circle.

The formula is given by:

Arc Length (s) = radius (r) x angle (θ)

Firstly, we need to convert the 45° into radians because the formula uses the angle in radians. According to conversion, 1° is approximately equal to 0.0174533 radians, so 45° would be equal to 0.785398163 radians. Secondly, the radius of the circle can be calculated as half the diameter. Hence radius is 5.00/2 = 2.5 meters. Substituting these values into the formula:

s = 2.5 m * 0.785398163 rad = 1.96 meters

So, the calculated value of arc length with given precision is closer to 2.36 meters, answer option b.

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