Find the area of a sector and arc length whose central angle is 0.5 radians and a radius of 10 inches.
Now wait a minute. You can look this up in your text or sketch it out on paper. There is no need to ask me.
for example
area of sector = (angle/2pi)area of circle
I am sure you can do that isoceles triangle in there
push down clutch, engage gears :)
To find the area of a sector, you need to use the formula:
Area of sector = (central angle / 2π) * π * r^2
where "central angle" is the angle in radians, and "r" is the radius of the circle.
In this case, the central angle is given as 0.5 radians and the radius is 10 inches. So, let's substitute these values into the formula:
Area of sector = (0.5 / 2π) * π * (10)^2
Simplifying the formula:
Area of sector = (0.5 / 2) * 100
Area of sector = 0.25 * 100
Area of sector = 25 square inches
So, the area of the sector is 25 square inches.
To find the arc length, you need to use the following formula:
Arc length = (central angle / 2π) * 2π * r
Using the given central angle of 0.5 radians and the radius of 10 inches, let's substitute these values into the formula:
Arc length = (0.5 / 2π) * 2π * 10
Simplifying the formula:
Arc length = (0.5 / 2) * 20
Arc length = (0.25) * 20
Arc length = 5 inches
So, the arc length is 5 inches.