Question

Please help i need this done by the next hour and i’m failing and struggling

3. The sector of a circle is shown below. It has a radius of 10 centimeters and a central
angle of 51 degrees. Find to the nearest tenth in both cases:
(a) the length of AB in centimeters(b) the area of the sector in square centimeters

1. An arc has a central angle of 1.8 radians and a radius of 20 inches. a. Determine the length of AB in inches
b. to the nearest degree what is the measure of

Answer 1

(1). 36 inch. , 103° ; (2). 8.9 cm , 44.5 cm² ;

Explanation:

1).

(b). m∠BCA = 1.8 rad. ×
`(180)/(\pi )` ≈ 103° ( π ≈
`(22)/(7)` )

(a). C = 2 π r , the length of arc AB = ( 2 ×
`(22)/(7)` × 20 ) ÷ 360° × 103.132° ≈ 36 inches

3).

(a). The length of arc AB = ( 2 ×
`(22)/(7)` × 10 ) ÷ 360° × 51° ≈ 8.9 cm

(b). A = π r² , the area of the sector = (
`(22)/(7)` × 10² ) ÷ 360° × 51° ≈ 44.5 cm²

Answer 2

Question 3)

`\stackrel{\frown}{AC}=36\text{ inches}`

`\angle BCA\approx103^\circ`

Question 1)

`\stackrel{\frown}{AB}\approx 8.9\text{ cm}\\`

`A\approx44.5\text{ cm}^2`

Explanation:

Question 3)

We are given that the central angle is 1.8 radians and has a radius of 20 inches.

Part A)

The formula for arc length in terms of radians is given by:

`s=r\theta`

Where s is the arc length, r is the radius, and θ is the angle in radians.

In this case, r is 20 and θ is 1.8. Hence, the arc length is:

`\stackrel{\frown}{AC}=(20)(1.8)=36\text{ inches}`

Part B)

∠BCA is the central angle that measures 1.8 radians.

We can convert radians to degrees using the following formula:

`\displaystyle d=\theta\cdot(180^\circ)/(\pi)`

Where d is the measure in degrees, and θ is the measure in radians.

Therefore:

`\displaystyle d=1.8\cdot(180^\circ)/(\pi)\approx103.1324\approx103^\circ`

Question 1)*

Part A)

We will use the arc length formula in degrees given by:

`\displaystyle s=2\pi r\cdot (\theta^\circ)/(360)`

Where r is the radius and θ is the angle measured in degrees.

We have a radius of 10 centimeters and a central angle of 51°. Therefore, our arc length is:

`\displaystyle \stackrel{\frown}{AB}=2\pi(10)\cdot(51)/(360)=20\pi\cdot(51)/(360)\approx8.9\text{ cm}`

Part B)

We will use the formula for the area of a sector in degrees given by:

`\displaystyle A=\pi r^2\cdot(\theta^\circ)/(360)`

So, we will substitute 10 for r and 51 for θ. Hence, the area of the sector is:

`\displaystyle A=\pi (10)^2\cdot (51)/(360)=100\pi\cdot(51)/(360)\approx44.5\text{ cm}^2`

*Notes:

For this question, it is possible and completely fine for us to convert 51° to radians and then use the formulas in terms of radians.