In this picture, the measure of angle is 1 radian.


In this picture, the measure of angle is 1 radian.

Answers

Wheres the pic?may u screen shot
To solve this, we are going to use the formula for the area of the sector of a circle: A= \frac{1}{2} r^2 \alpha
where
A is the area of the circular sector.
r is the radius of the circle.
 \alpha is the central angle in radians.

We know form our problem that that the measure of the central angle is 1 radian, so  \alpha =1. We can also infer from the picture that the radius of the circle is 3in, so r=3in. Lets replace those values in our formula to find A:
A= \frac{1}{2} r^2 \alpha
A= \frac{1}{2} (3in)^2(1)
A=4.5in^2

We can conclude that the area of the circular sector in the picture is 4.5 square inches.

To prove that the arc length is indeed 3 inches, we are going to use the formula: A_{L}=r \alpha
where
A_{L} is the arc length.
r us the radius of the circle.
 \alpha is the central angle.

We know from our problem that r=3in, and  \alpha =1, so lets replace those values in our formula:
A_{L}=r \alpha
A_{L}=(3in) \alpha
A_{L}=3in

We can conclude that the length of the arc is indeed 3 inches.
To solve this, we are going to use the formula for the area of the sector of a circle: A= \frac{1}{2} r^2 \alpha
where
A is the area of the circular sector.
r is the radius of the circle.
\alpha is the central angle in radians.

We know form our problem that that the measure of the central angle is 1 radian, so \alpha =1. We can also infer from the picture that the radius of the circle is 3in, so r=3in. Lets replace those values in our formula to find A:
A= \frac{1}{2} r^2 \alpha
A= \frac{1}{2} (3in)^2(1)
A=4.5in^2

We can conclude that the area of the circular sector in the picture is 4.5 square inches.

To prove that the arc length is indeed 3 inches, we are going to use the formula: A_{L}=r \alpha
where
A_{L} is the arc length.
r us the radius of the circle.
\alpha is the central angle.

We know from our problem that r=3in, and \alpha =1, so lets replace those values in our formula:
A_{L}=r \alpha
A_{L}=(3in) \alpha
A_{L}=3in

We can conclude that the length of the arc is indeed 3 inches.

True.                                  

Step-by-step explanation:

the answere for this question is false

False

Step-by-step explanation:

Radius of circle = r = 2.5 in

Length of arc of the circle = s = 2 in

Central angle in radians = θ

The length of arc of the circle is the product of the radius and the central angle in radians.

s = rθ

\theta=\frac{s}{r}\\\Rightarrow \theta=\frac{2}{2.5}\\\Rightarrow \theta=0.8\ radians

θ = 0.8 radians

The measure of angle θ is not 1 radian but 0.8 radian.

False



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