Finding the Central Angle in a Circle

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Question 1 of 4

1. Question
Find the value of $θ$ $theta$
- $θ =$ $theta=$ (1)
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Arc Length Formula

$l$ $l$ $=$ $=$ $r$ $r$ $θ$ $theta$

Substitute the known values and solve for $θ$ $theta$

$l$ $l$ $=$ $=$ $8$ $8$

$r$ $r$ $=$ $=$ $8$ $8$

$l$ $l$ $=$ $=$ $r$ $r$ $θ$ $theta$

$8$ $8$ $=$ $=$ $8$ $8$ $θ$ $theta$ Substitute known values

$8$ $8$ $\div 8$ $divide8$ $=$ $=$ $8 θ$ $8theta$ $\div 8$ $divide8$ Divide both sides by $8$ $8$

$1$ $1$ $=$ $=$ $θ$ $theta$

$θ$ $theta$ $=$ $=$ $1$ $1$

$θ = 1$ $theta=1$
Question 2 of 4

2. Question
Find the value of $θ$ $theta$
- $θ =$ $theta=$ (1.8)
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Arc Length Formula

$l$ $l$ $=$ $=$ $r$ $r$ $θ$ $theta$

Substitute the known values and solve for $θ$ $theta$

$l$ $l$ $=$ $=$ $9$ $9$

$r$ $r$ $=$ $=$ $5$ $5$

$l$ $l$ $=$ $=$ $r$ $r$ $θ$ $theta$

$9$ $9$ $=$ $=$ $5$ $5$ $θ$ $theta$ Substitute known values

$9$ $9$ $\div 5$ $divide5$ $=$ $=$ $5 θ$ $5theta$ $\div 5$ $divide5$ Divide both sides by $5$ $5$

$1.8$ $1.8$ $=$ $=$ $θ$ $theta$

$θ$ $theta$ $=$ $=$ $1.8$ $1.8$

$θ = 1.8$ $theta=1.8$

Question 3 of 4

Find the value of

θ

$theta$

Use

π = 3.14

$pi=3.14$

$θ =$ $theta=$ (1.88)

Question 4 of 4

Given that

A = 300 {cm}^{2}

$A=300\text(cm)^2$ , find the value of

θ

$theta$ in degrees

Use

π = 3.1415

$pi=3.1415$
Round your answer to one decimal place

$θ =$ $theta=$ (14.7) $°$ $°$

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Arc Length Formula

$l$ $l$

=

$=$ $r$ $r$ $θ$ $theta$

Area of a Circle Formula

A = π r^{2}

$A=\pi\color{#9a00c7}{r}^2$

Converting Radian to Degrees

degrees = radian \times \frac{180 °}{π}

$\text(degrees)=\text(radian)xx(180°)/pi$

First, use the area of a circle formula and solve for $r$ $r$

Area

$\text(Area)$

=

$=$

300

$300$

$Area$ $\text(Area)$	$=$ $=$	$\pi\color{#9a00c7}{r}^2$
$300$ $300$	$=$ $=$	$\pi\color{#9a00c7}{r}^2$	Substitute known values
$300$ $300$ $\div π$ $divide pi$	$=$ $=$	$π r^{2}$ $pi r^2$ $\div π$ $divide pi$	Divide both sides by $π$ $pi$

$\sqrt{\frac{300}{π}}$ $sqrt(300/(pi))$	$=$ $=$	$\sqrt{r^{2}}$ $sqrt(r^2)$	Find the square root of both sides

$9.772$ $9.772$	$=$ $=$	$r$ $r$
$r$ $r$	$=$ $=$	$9.772$ $9.772$

Next, substitute the known values and solve for

θ

$theta$

$l$ $l$	$=$ $=$	$2.5$ $2.5$
$r$ $r$	$=$ $=$	$9.772$ $9.772$

$l$ $l$	$=$ $=$	$r$ $r$ $θ$ $theta$
$2.5$ $2.5$	$=$ $=$	$9.772$ $9.772$ $θ$ $theta$	Substitute known values
$2.5$ $2.5$ $\div 9.772$ $divide9.772$	$=$ $=$	$9.772 θ$ $9.772theta$ $\div 9.772$ $divide9.772$	Divide both sides by $9.772$ $9.772$
$0.2558$ $0.2558$	$=$ $=$	$θ$ $theta$
$θ$ $theta$	$=$ $=$	$0.2558$ $0.2558$

Finally, convert the radian to degrees

$degrees$ $\text(degrees)$	$=$ $=$	$radians \times \frac{180 °}{π}$ $\text(radians)xx(180°)/pi$

	$=$ $=$	$0.2558 \times \frac{180 °}{π}$ $0.2558xx(180°)/pi$

	$=$ $=$	$\frac{46.044 °}{3.1415}$ $(46.044°)/(3.1415)$	Use $π = 3.1415$ $pi=3.1415$

	$=$ $=$	$14.7°$	Rounded to one decimal place

$theta=14.7°$

$2 π -$ $2pi-$ $4.4$ $4.4$	$=$ $=$	$(2 \times 3.14) - 4.4$ $(2xx3.14)-4.4$
	$=$ $=$	$6.28 - 4.4$ $6.28-4.4$
	$=$ $=$	$1.88$ $1.88$

Finding the Central Angle in a Circle

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Quiz summary

Information

1. Question

Hint

Excellent!

Arc Length Formula

2. Question

Hint

Fantastic!

Arc Length Formula

3. Question

Hint

Well Done!

Arc Length Formula

4. Question

Hint

Great Work!

Arc Length Formula

Area of a Circle Formula

Converting Radian to Degrees

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