A sector has an area of 150cm22 squared.Given a radius of 20cm, what is the angle subtended by the sector?Give your answer correct to the nearest degree.
Question
A sector has an area of 150 cm².
Given a radius of 20 cm, what is the angle subtended by the sector?
Give your answer correct to the nearest degree.
Solution
The formula for the area of a sector is given by:
Area = 0.5 * r² * θ
where r is the radius and θ is the angle in radians.
We can rearrange this formula to solve for θ:
θ = Area / (0.5 * r²)
Substituting the given values:
θ = 150 / (0.5 * 20²)
θ = 150 / 200 = 0.75 radians
To convert radians to degrees, we multiply by 180/π:
θ = 0.75 * 180/π ≈ 43 degrees
So, the angle subtended by the sector is approximately 43 degrees.
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