Given that a circle has a radius of 7cm and an arc of length 9cm is subtended by a central angle 𝜃, find the measure of 𝜃 in degrees. Give your answer to 3 significant figures without the symbol ∘ or the word ‘degrees’.
Question
Given that a circle has a radius of 7cm and an arc of length 9cm is subtended by a central angle 𝜃, find the measure of 𝜃 in degrees. Give your answer to 3 significant figures without the symbol ∘ or the word ‘degrees’.
Solution
The measure of the central angle θ in degrees can be found using the formula:
θ = (L / 2πr) * 360
where: L is the length of the arc, r is the radius of the circle, and 360 is the total degrees in a circle.
Substituting the given values:
θ = (9 cm / 2π * 7 cm) * 360 = 73.304 degrees
So, the measure of θ to 3 significant figures is 73.3.
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