Final answer:
The length of a side of the pentagon inscribed in a circle with a radius of 4.5 cm is approximately 14 mm or 1.4 cm, calculated using the formula for the chord length in relation to the circle's radius and the angle subtended by the chord.
Step-by-step explanation:
To find the length of a side of a regular pentagon inscribed in a circle of radius 4.5 cm, we can use trigonometry. A regular pentagon has five sides of equal length and subtends an angle of 72° at the center of the circle for each segment. Using the formula for the length of a chord given the radius (r) and the subtended angle (θ) in radians, which is Chord length = 2 × r × sin(θ/2), we can calculate the length of a side of the pentagon.
The subtended angle in radians is θ = 72° × (π/180°) = 1.25664 radians. Plugging the values into the formula, we have:
Chord length = 2 × 4.5 cm × sin(1.25664/2) = 2 × 4.5 cm × sin(0.62832) ≈ 13.9032 mm, which rounds to 14 mm or 1.4 cm when converted to centimeters.