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

Answer:

Question 3)

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

$\angle BCA\approx103^\circ$

Question 1)

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

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

Step-by-step 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:

$\displaystyle d=\theta\cdot\frac{180^\circ}{\pi}$

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

Therefore:

$\displaystyle d=1.8\cdot\frac{180^\circ}{\pi}\approx103.1324\approx103^\circ$

Question 1)*

Part A)

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

$\displaystyle s=2\pi r\cdot \frac{\theta^\circ}{360}$

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:

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

Part B)

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

$\displaystyle A=\pi r^2\cdot\frac{\theta^\circ}{360}$

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

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

*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.

Answer 2

Answer:

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

Step-by-step explanation:

1).

(b). m∠BCA = 1.8 rad. × $\frac{180}{\pi }$ ≈ 103° ( π ≈ $\frac{22}{7}$ )

(a). C = 2 π r , the length of arc AB = ( 2 × $\frac{22}{7}$ × 20 ) ÷ 360° × 103.132° ≈ 36 inches

3).

(a).  The length of arc AB = ( 2 × $\frac{22}{7}$ × 10 ) ÷ 360° × 51° ≈ 8.9 cm

(b). A = π r² , the area of the sector = ( $\frac{22}{7}$ × 10² ) ÷ 360° × 51° ≈ 44.5 cm²