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An intercepted arc has a length of 19 yards. If the radius is 4 yards, find the measure of the central angle in radians and degrees.

Sagot :

Answer:

19*4=76

Step-by-step explanation:

The length of an arc is the distance between the endpoints of the arc.

The central angle is: [tex]\mathbf{4.75\ rad}[/tex] or [tex]\mathbf{272.16^o}[/tex]

The given parameters are:

[tex]\mathbf{l = 19yd}[/tex] --- length of the arc

[tex]\mathbf{r = 4}[/tex] -- radius of the circle

The length of an arc is calculated as:

[tex]\mathbf{l =r\theta}[/tex]

Divide both sides by r

[tex]\mathbf{\theta = \frac lr}[/tex]

Substitute known values

[tex]\mathbf{\theta = \frac{19}4}[/tex]

[tex]\mathbf{\theta = 4.75\ radians}[/tex]

Convert to degrees as follows:

[tex]\mathbf{\theta = 4.75 \times \frac{180}{\pi}}[/tex]

[tex]\mathbf{\theta = 4.75 \times \frac{180}{3.142}}[/tex]

[tex]\mathbf{\theta = 272.16^o}[/tex]

Hence, the central angle is: [tex]\mathbf{4.75\ rad}[/tex] or [tex]\mathbf{272.16^o}[/tex]

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