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A sector in a circle of radius 25 ft has an area of 125 ft². Find the central angle of the sector.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
The area of a circular sector is given by the formula
where A is the area of a circular sector, R is the radius of a circular sector, and θ is the central angle of circular sector in radians. Radians is a unit less value of an angle.
Substitute the values of A and R in order to solve for the value of central angle, as follows
You can also express the value of central angle in degrees, as follows
