Answer :
Answer: What is the measure of the central angle? 140
What ratio represents the measure of the central angle compared to the measure of the entire circle? 7/18
If s = StartFraction theta Over 360 degrees EndFraction (2 pi r), what is the length of minor arc AB? 14π
Step-by-step explanation: Just did it.
1) the measure of the central angle ∠ACB = 140°
2) the ratio 7:18 represents the measure of the central angle compared to the measure of the entire circle.
3) the length of the minor arc AB 23.4 units.
What is central angle?
"It is the angle that forms when two radii meet at the center of a circle."
What is chord of a circle?
"It is the line segment joining any two points on the circumference of the circle. "
Formula to calculate chord length:
Chord Length = 2 × r × sin(c/2)
where r: radius of the circle
c: central angle
For given example,
Line segments AC and BC are radii.
The length of CB is 18.
Angle A C B is 140 degrees.
Consider the following figure.
From given information,
Chord length (CB) = 18
Central angle (c) = 140°
Using the formula of chord length we find the radius (r) of the circle C.
⇒ CB = 2 × r × sin(c/2)
⇒ 18 = 2 × r × sin(140/2)
⇒ 18 = 2 × 0.9396 × r
⇒ r = (18)/(1.8792)
⇒ r = 9.58
⇒ AC = 9.58 and BC = 9.58
1) the measure of the central angle:
Here, ∠ACB is the central angle.
the measure of the central angle ∠ACB = 140°
2) We know, the measure of the entire circle is 360°
So, the ratio that represents the measure of the central angle compared to the measure of the entire circle would be,
140/360 = 7/18
Therefore, the ratio 7:18 represents the measure of the central angle compared to the measure of the entire circle.
3) [tex]s=\frac{\theta}{360^{\circ}}\times 2\times \pi \times r[/tex]
We need to find the length of the minor arc AB
The central angle for minor arc AB is [tex]\theta=140^{\circ}[/tex]
r = 9.58 units
[tex]\Rightarrow s=\frac{140}{360^{\circ}}\times 2\times \pi \times 9.58\\\\ \Rightarrow s = 23.39\\\\ \Rightarrow \bold{s = 23.4}~~units[/tex]
Therefore, the length of the minor arc AB 23.4 units.
Learn more about arc of the circle here:
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