Math / Geometry

QuestionQuestion Watch Video Show Examples
In a circle with radius 5 , an angle measuring $\frac{\pi}{6}$ radians intercepts an arc. Find the length of the arc in simplest form.

Studdy Solution

STEP 1

1. The circle has a radius of $5$ .
2. The angle intercepting the arc measures $\frac{\pi}{6}$ radians.
3. We need to find the length of the arc.

STEP 2

1. Recall the formula for the arc length.
2. Substitute the given values.
3. Calculate the arc length.

STEP 3

Recall the formula for the arc length:
$\text{Arc Length} = \theta \times r$
where $\theta$ is the angle in radians and $r$ is the radius of the circle.

STEP 4

Substitute the given values into the formula:
$\text{Arc Length} = \frac{\pi}{6} \times 5$

STEP 5

Calculate the product:
$\text{Arc Length} = \frac{\pi}{6} \times 5$ $= \frac{5\pi}{6}$
The length of the arc is:
$\boxed{\frac{5\pi}{6}}$

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QuestionQuestion Watch Video Show Examples
In a circle with radius 5 , an angle measuring $\frac{\pi}{6}$ radians intercepts an arc. Find the length of the arc in simplest form.

Studdy Solution

STEP 1

1. The circle has a radius of $5$ .
2. The angle intercepting the arc measures $\frac{\pi}{6}$ radians.
3. We need to find the length of the arc.

STEP 2

1. Recall the formula for the arc length.
2. Substitute the given values.
3. Calculate the arc length.

STEP 3

Recall the formula for the arc length:
$\text{Arc Length} = \theta \times r$
where $\theta$ is the angle in radians and $r$ is the radius of the circle.

STEP 4

Substitute the given values into the formula:
$\text{Arc Length} = \frac{\pi}{6} \times 5$

STEP 5

Calculate the product:
$\text{Arc Length} = \frac{\pi}{6} \times 5$ $= \frac{5\pi}{6}$
The length of the arc is:
$\boxed{\frac{5\pi}{6}}$

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QuestionQuestion Watch Video Show ExamplesIn a circle with radius 5 , an angle measuring π6\frac{\pi}{6}6π​ radians intercepts an arc. Find the length of the arc in simplest form.

Studdy Solution

STEP 1

1. The circle has a radius of 5 5 5.2. The angle intercepting the arc measures π6 \frac{\pi}{6} 6π​ radians.3. We need to find the length of the arc.

STEP 2

1. Recall the formula for the arc length.2. Substitute the given values.3. Calculate the arc length.

STEP 3

Recall the formula for the arc length:Arc Length=θ×r \text{Arc Length} = \theta \times r Arc Length=θ×rwhere θ \theta θ is the angle in radians and r r r is the radius of the circle.

STEP 4

Substitute the given values into the formula:Arc Length=π6×5 \text{Arc Length} = \frac{\pi}{6} \times 5 Arc Length=6π​×5

STEP 5

Calculate the product:Arc Length=π6×5 \text{Arc Length} = \frac{\pi}{6} \times 5 Arc Length=6π​×5 =5π6 = \frac{5\pi}{6} =65π​ The length of the arc is:5π6 \boxed{\frac{5\pi}{6}} 65π​​

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Studdy solves anything!

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QuestionQuestion Watch Video Show Examples
In a circle with radius 5 , an angle measuring $\frac{\pi}{6}$ radians intercepts an arc. Find the length of the arc in simplest form.

1. The circle has a radius of $5$ .
2. The angle intercepting the arc measures $\frac{\pi}{6}$ radians.
3. We need to find the length of the arc.

1. Recall the formula for the arc length.
2. Substitute the given values.
3. Calculate the arc length.

Recall the formula for the arc length:
$\text{Arc Length} = \theta \times r$
where $\theta$ is the angle in radians and $r$ is the radius of the circle.

Substitute the given values into the formula:
$\text{Arc Length} = \frac{\pi}{6} \times 5$

Calculate the product:
$\text{Arc Length} = \frac{\pi}{6} \times 5$ $= \frac{5\pi}{6}$
The length of the arc is:
$\boxed{\frac{5\pi}{6}}$