Arc Length - Trigonometry

Card 1 of 32

Didn't Know

Knew It

1 of 2019 left

Question

True or False: You are given the central angle measure but no other information, you are able to solve for the arc length.

Tap to reveal answer

Answer

We do not have enough information to solve for the arc length. We know that the measure of the arc is equal to the central angle and that the measure of the arc is $\theta = $\frac{r}{l_A}$$ but we still have two unknowns with no method to solve for them.

← Didn't Know|Knew It →

Question

Which is true of the relationship between the arc measure and the central angle as shown below?

Tap to reveal answer

Answer

Every arc has a measure that is equal to the measure of the central angle that creates the arc. This is because the measure of the angle determines the distance around the circumference that the arc makes.

← Didn't Know|Knew It →

Question

Which of the following is the correct formula for finding arc length?

Tap to reveal answer

Answer

The circumference of an entire circle is $2\pi r$ . When considering the length of an arc, the angle is less than $2\pi$ denoted by angle $\theta$ . So the formula for finding the length of an arc is replacing the angle of an entire circle, $2\pi$ , with the angle that forms the arc, $\theta$ . This gives us the formula $l_A = \theta r$ .

← Didn't Know|Knew It →

Question

Which of the following is the correct arc length formed by the angle $\frac{\pi}{3}$ of a circle whose radius is a length of 5?

Tap to reveal answer

Answer

We must use the formula for finding arc length $l_A = \theta r$ . We have been given all the information needed to just plug into the formula.

$l_A = \theta r$

$l_A = $\frac{\pi}{3}$ 5$

$l_A = $\frac{5\pi}{3}$$

← Didn't Know|Knew It →

Question

Which of the following is the correct arc length formed by an angle with measure 30 degrees of a circle whose radius is a length of 3?

Tap to reveal answer

Answer

First, we are given our angle measure in degrees and we must convert to radians to be able to use our arc length formula.

$30 $\frac{\pi}{180}$ = $\frac{\pi}{6}$$

Now we are able to plug the radius length and the angle measure into our formula and solve for the arc length.

$l_A = $\frac{\pi}{6}$ 3$

$l_A = $\frac{3\pi}{6}$$

$l_A = $\frac{\pi}{2}$$

← Didn't Know|Knew It →

Question

What is the measure of the angle that forms an arc with length 2.33 of a circle who has radius 4? Round to the second decimal place.

Tap to reveal answer

Answer

We must use the formula for finding arc length to solve for the measure of the angle, $\theta$ . The formula is $l_A = \theta r$ .

$l_A = \theta r$

$2.33 = \theta 4$

$0.58 = \theta$

← Didn't Know|Knew It →

Question

An arc has a measure of $\frac{\pi}{4}$ and a diameter of 7, what is the measure of the central angle?

Tap to reveal answer

Answer

Notice the question gave you the measure of the arc, NOT the arc length. The measure of an arc is equal to the measure of the central angle that forms the arc. We do not even need to use our formula for this one, just the fact that the central angle is equal to the measure of the arc that it forms.

← Didn't Know|Knew It →

Question

You know that the central angle of a sector is $\frac{3\pi}{2}$ and the sector area is $\frac{7\pi}{4}$ , what is the arc length? Round to two decimals.

Tap to reveal answer

Answer

The formula to find the area of a sector is $A = $\frac{\theta}{2}$ $r^2$$ . The piece of information we are missing to solve for arc length is the radius, so we will use the formula for finding the area of a sector to solve for radius, allowing us to solve for the arc length.

$A = $\frac{\theta}{2}$ $r^2$$

$\frac{7\pi}{4}$ = $($\frac{3\pi}$){2}($\frac{1}{2}$)r^2$

$\frac{7\pi}{4}$ = ($\frac{3\pi}{4}$ $r^2$

$\frac{7\pi}{3}$ = $r^2$

$$\sqrt{\frac{7\pi}{3}$} = r$

Now we can plug this into our formula to solve for arc length

$l_A = \theta r$

$l_A = $\frac{3\pi}{2}$ (2.707)$

← Didn't Know|Knew It →

Question

Which is true of the relationship between the arc measure and the central angle as shown below?

Tap to reveal answer

Answer

Every arc has a measure that is equal to the measure of the central angle that creates the arc. This is because the measure of the angle determines the distance around the circumference that the arc makes.

← Didn't Know|Knew It →

Question

Which of the following is the correct formula for finding arc length?

Tap to reveal answer

Answer

The circumference of an entire circle is $2\pi r$ . When considering the length of an arc, the angle is less than $2\pi$ denoted by angle $\theta$ . So the formula for finding the length of an arc is replacing the angle of an entire circle, $2\pi$ , with the angle that forms the arc, $\theta$ . This gives us the formula $l_A = \theta r$ .

← Didn't Know|Knew It →

Question

Which of the following is the correct arc length formed by the angle $\frac{\pi}{3}$ of a circle whose radius is a length of 5?

Tap to reveal answer

Answer

We must use the formula for finding arc length $l_A = \theta r$ . We have been given all the information needed to just plug into the formula.

$l_A = \theta r$

$l_A = $\frac{\pi}{3}$ 5$

$l_A = $\frac{5\pi}{3}$$

← Didn't Know|Knew It →

Question

Which of the following is the correct arc length formed by an angle with measure 30 degrees of a circle whose radius is a length of 3?

Tap to reveal answer

Answer

First, we are given our angle measure in degrees and we must convert to radians to be able to use our arc length formula.

$30 $\frac{\pi}{180}$ = $\frac{\pi}{6}$$

Now we are able to plug the radius length and the angle measure into our formula and solve for the arc length.

$l_A = $\frac{\pi}{6}$ 3$

$l_A = $\frac{3\pi}{6}$$

$l_A = $\frac{\pi}{2}$$

← Didn't Know|Knew It →

Question

What is the measure of the angle that forms an arc with length 2.33 of a circle who has radius 4? Round to the second decimal place.

Tap to reveal answer

Answer

We must use the formula for finding arc length to solve for the measure of the angle, $\theta$ . The formula is $l_A = \theta r$ .

$l_A = \theta r$

$2.33 = \theta 4$

$0.58 = \theta$

← Didn't Know|Knew It →

Question

An arc has a measure of $\frac{\pi}{4}$ and a diameter of 7, what is the measure of the central angle?

Tap to reveal answer

Answer

Notice the question gave you the measure of the arc, NOT the arc length. The measure of an arc is equal to the measure of the central angle that forms the arc. We do not even need to use our formula for this one, just the fact that the central angle is equal to the measure of the arc that it forms.

← Didn't Know|Knew It →

Question

True or False: You are given the central angle measure but no other information, you are able to solve for the arc length.

Tap to reveal answer

Answer

We do not have enough information to solve for the arc length. We know that the measure of the arc is equal to the central angle and that the measure of the arc is $\theta = $\frac{r}{l_A}$$ but we still have two unknowns with no method to solve for them.

← Didn't Know|Knew It →

Question

You know that the central angle of a sector is $\frac{3\pi}{2}$ and the sector area is $\frac{7\pi}{4}$ , what is the arc length? Round to two decimals.

Tap to reveal answer

Answer

The formula to find the area of a sector is $A = $\frac{\theta}{2}$ $r^2$$ . The piece of information we are missing to solve for arc length is the radius, so we will use the formula for finding the area of a sector to solve for radius, allowing us to solve for the arc length.

$A = $\frac{\theta}{2}$ $r^2$$

$\frac{7\pi}{4}$ = $($\frac{3\pi}$){2}($\frac{1}{2}$)r^2$

$\frac{7\pi}{4}$ = ($\frac{3\pi}{4}$ $r^2$

$\frac{7\pi}{3}$ = $r^2$

$$\sqrt{\frac{7\pi}{3}$} = r$

Now we can plug this into our formula to solve for arc length

$l_A = \theta r$

$l_A = $\frac{3\pi}{2}$ (2.707)$

← Didn't Know|Knew It →

Question

Which is true of the relationship between the arc measure and the central angle as shown below?

Tap to reveal answer

Answer

Every arc has a measure that is equal to the measure of the central angle that creates the arc. This is because the measure of the angle determines the distance around the circumference that the arc makes.

← Didn't Know|Knew It →

Question

Which of the following is the correct formula for finding arc length?

Tap to reveal answer

Answer

The circumference of an entire circle is $2\pi r$ . When considering the length of an arc, the angle is less than $2\pi$ denoted by angle $\theta$ . So the formula for finding the length of an arc is replacing the angle of an entire circle, $2\pi$ , with the angle that forms the arc, $\theta$ . This gives us the formula $l_A = \theta r$ .

← Didn't Know|Knew It →

Question

Which of the following is the correct arc length formed by the angle $\frac{\pi}{3}$ of a circle whose radius is a length of 5?

Tap to reveal answer

Answer

We must use the formula for finding arc length $l_A = \theta r$ . We have been given all the information needed to just plug into the formula.

$l_A = \theta r$

$l_A = $\frac{\pi}{3}$ 5$

$l_A = $\frac{5\pi}{3}$$

← Didn't Know|Knew It →

Question

Which of the following is the correct arc length formed by an angle with measure 30 degrees of a circle whose radius is a length of 3?

Tap to reveal answer

Answer

First, we are given our angle measure in degrees and we must convert to radians to be able to use our arc length formula.

$30 $\frac{\pi}{180}$ = $\frac{\pi}{6}$$

Now we are able to plug the radius length and the angle measure into our formula and solve for the arc length.

$l_A = $\frac{\pi}{6}$ 3$

$l_A = $\frac{3\pi}{6}$$

$l_A = $\frac{\pi}{2}$$

← Didn't Know|Knew It →

Knew It

Arc Length - Trigonometry

True or False: You are given the central angle measure but no other information, you are able to solve for the arc length.

We do not have enough information to solve for the arc length. We know that the measure of the arc is equal to the central angle and that the measure of the arc is but we still have two unknowns with no method to solve for them.

Which is true of the relationship between the arc measure and the central angle as shown below?

Every arc has a measure that is equal to the measure of the central angle that creates the arc. This is because the measure of the angle determines the distance around the circumference that the arc makes.

Which of the following is the correct formula for finding arc length?

The circumference of an entire circle is . When considering the length of an arc, the angle is less than denoted by angle . So the formula for finding the length of an arc is replacing the angle of an entire circle, , with the angle that forms the arc, . This gives us the formula .

Which of the following is the correct arc length formed by the angle of a circle whose radius is a length of 5?

We must use the formula for finding arc length . We have been given all the information needed to just plug into the formula.

Which of the following is the correct arc length formed by an angle with measure 30 degrees of a circle whose radius is a length of 3?

First, we are given our angle measure in degrees and we must convert to radians to be able to use our arc length formula. Now we are able to plug the radius length and the angle measure into our formula and solve for the arc length.

What is the measure of the angle that forms an arc with length 2.33 of a circle who has radius 4? Round to the second decimal place.

We must use the formula for finding arc length to solve for the measure of the angle, . The formula is .

An arc has a measure of and a diameter of 7, what is the measure of the central angle?

Notice the question gave you the measure of the arc, NOT the arc length. The measure of an arc is equal to the measure of the central angle that forms the arc. We do not even need to use our formula for this one, just the fact that the central angle is equal to the measure of the arc that it forms.

You know that the central angle of a sector is and the sector area is , what is the arc length? Round to two decimals.

Which is true of the relationship between the arc measure and the central angle as shown below?

Every arc has a measure that is equal to the measure of the central angle that creates the arc. This is because the measure of the angle determines the distance around the circumference that the arc makes.

Which of the following is the correct formula for finding arc length?

The circumference of an entire circle is . When considering the length of an arc, the angle is less than denoted by angle . So the formula for finding the length of an arc is replacing the angle of an entire circle, , with the angle that forms the arc, . This gives us the formula .

Which of the following is the correct arc length formed by the angle of a circle whose radius is a length of 5?

We must use the formula for finding arc length . We have been given all the information needed to just plug into the formula.

Which of the following is the correct arc length formed by an angle with measure 30 degrees of a circle whose radius is a length of 3?

First, we are given our angle measure in degrees and we must convert to radians to be able to use our arc length formula. Now we are able to plug the radius length and the angle measure into our formula and solve for the arc length.

What is the measure of the angle that forms an arc with length 2.33 of a circle who has radius 4? Round to the second decimal place.

We must use the formula for finding arc length to solve for the measure of the angle, . The formula is .

An arc has a measure of and a diameter of 7, what is the measure of the central angle?

Notice the question gave you the measure of the arc, NOT the arc length. The measure of an arc is equal to the measure of the central angle that forms the arc. We do not even need to use our formula for this one, just the fact that the central angle is equal to the measure of the arc that it forms.

True or False: You are given the central angle measure but no other information, you are able to solve for the arc length.

We do not have enough information to solve for the arc length. We know that the measure of the arc is equal to the central angle and that the measure of the arc is but we still have two unknowns with no method to solve for them.

You know that the central angle of a sector is and the sector area is , what is the arc length? Round to two decimals.

Which is true of the relationship between the arc measure and the central angle as shown below?

Every arc has a measure that is equal to the measure of the central angle that creates the arc. This is because the measure of the angle determines the distance around the circumference that the arc makes.

Which of the following is the correct formula for finding arc length?

The circumference of an entire circle is . When considering the length of an arc, the angle is less than denoted by angle . So the formula for finding the length of an arc is replacing the angle of an entire circle, , with the angle that forms the arc, . This gives us the formula .

Which of the following is the correct arc length formed by the angle of a circle whose radius is a length of 5?

We must use the formula for finding arc length . We have been given all the information needed to just plug into the formula.

Which of the following is the correct arc length formed by an angle with measure 30 degrees of a circle whose radius is a length of 3?

First, we are given our angle measure in degrees and we must convert to radians to be able to use our arc length formula. Now we are able to plug the radius length and the angle measure into our formula and solve for the arc length.

We do not have enough information to solve for the arc length. We know that the measure of the arc is equal to the central angle and that the measure of the arc is $\theta = $\frac{r}{l_A}$$ but we still have two unknowns with no method to solve for them.

Which of the following is the correct arc length formed by the angle $\frac{\pi}{3}$ of a circle whose radius is a length of 5?

We must use the formula for finding arc length $l_A = \theta r$ . We have been given all the information needed to just plug into the formula.

$l_A = \theta r$

$l_A = $\frac{\pi}{3}$ 5$

$l_A = $\frac{5\pi}{3}$$

We must use the formula for finding arc length to solve for the measure of the angle, $\theta$ . The formula is $l_A = \theta r$ .

$l_A = \theta r$

$2.33 = \theta 4$

$0.58 = \theta$

An arc has a measure of $\frac{\pi}{4}$ and a diameter of 7, what is the measure of the central angle?

You know that the central angle of a sector is $\frac{3\pi}{2}$ and the sector area is $\frac{7\pi}{4}$ , what is the arc length? Round to two decimals.

Which of the following is the correct arc length formed by the angle $\frac{\pi}{3}$ of a circle whose radius is a length of 5?

We must use the formula for finding arc length $l_A = \theta r$ . We have been given all the information needed to just plug into the formula.

$l_A = \theta r$

$l_A = $\frac{\pi}{3}$ 5$

$l_A = $\frac{5\pi}{3}$$

We must use the formula for finding arc length to solve for the measure of the angle, $\theta$ . The formula is $l_A = \theta r$ .

$l_A = \theta r$

$2.33 = \theta 4$

$0.58 = \theta$

An arc has a measure of $\frac{\pi}{4}$ and a diameter of 7, what is the measure of the central angle?

We do not have enough information to solve for the arc length. We know that the measure of the arc is equal to the central angle and that the measure of the arc is $\theta = $\frac{r}{l_A}$$ but we still have two unknowns with no method to solve for them.

You know that the central angle of a sector is $\frac{3\pi}{2}$ and the sector area is $\frac{7\pi}{4}$ , what is the arc length? Round to two decimals.

Which of the following is the correct arc length formed by the angle $\frac{\pi}{3}$ of a circle whose radius is a length of 5?

We must use the formula for finding arc length $l_A = \theta r$ . We have been given all the information needed to just plug into the formula.

$l_A = \theta r$

$l_A = $\frac{\pi}{3}$ 5$

$l_A = $\frac{5\pi}{3}$$