The length of the arc PQ is 8.1 inches.
The arc length of a circle is calculated using the formula, s = rθ, where, s is the arc length, r is the radius of the circle, and θ is the angle (in radians) that the arc subtends at the center of the circle.
In the question, we are asked to find the length of the arc PQ.
The radius, r of the given circle is given to be 6.48 inches.
We assume the angle by arc PQ to be θ.
The total angle at the center is 360°.
Thus, Angle by arc PQ + Angle by arc QR + Angle by arc RS + Angle by arc SP = 360°,
or, θ + 65° + 150° + 73° = 360°,
or, θ + 288° = 360°,
or, θ = 360° - 288° = 72° = 72π/180 radians = 72*3.14/180 radians = 1.256 radians.
Thus, the length of the arc PQ, s = rθ = 6.48*1.256 inches = 8.13888 inches ≈ 8.1 inches.
Thus, the length of the arc PQ is 8.1 inches.
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