Find the radius of a circle in which the central angle, alpha, intercepts an arc of the given length alpha=60^(@),s=95" in " The radius is ◻ in. (Round to the nearest hundredth as needed.)

Identify Relationship: Identify the relationship between the arc length (s), the radius (r), and the central angle (α) in degrees. The formula that relates these three variables is s = r * α * (π/180), where α is in degrees.Substitute Values: Substitute the given values into the formula. Given that α = 60 degrees and s = 95 inches, we can substitute these values into the formula to find the radius r. 95 = r * 60 * (π/180)Simplify Equation: Simplify the equation to solve for r. First, simplify the right side of the equation by multiplying 60 by π/180, which simplifies to π/3. 95 = r * (π/3) Now, to solve for r, divide both sides of the equation by π/3. r = 95 / (π/3)Calculate Radius: Calculate the value of r. r = 95 / (π/3) = 95 * (3/π) ≈ 95 * (3/3.14159) ≈ 95 * 0.95493 ≈ 90.71835 Round the result to the nearest hundredth. r ≈ 90.72 inches

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the radius of a circle in which the central angle,
alpha, intercepts an arc of the given length

alpha=60^(@),s=95" in "
The radius is
◻ in.
(Round to the nearest hundredth as needed.)

Find the radius of a circle in which the central angle, $\alpha$ , intercepts an arc of the given length $\newline$ $\alpha=60^{\circ}, \mathrm{s}=95 \text { in }$ $\newline$ The radius is $\square$ in. $\newline$ (Round to the nearest hundredth as needed.)

View step-by-step help

Home

Math Problems

Algebra 2

Find Coordinate on Unit Circle

Full solution

Q. Find the radius of a circle in which the central angle,

\alpha

, intercepts an arc of the given length

\newline

\alpha=60^{\circ}, \mathrm{s}=95 \text { in }

\newline

The radius is

\square

in.

\newline

(Round to the nearest hundredth as needed.)

Identify Relationship: Identify the relationship between the arc length ( $s$ ), the radius ( $r$ ), and the central angle ( $\alpha$ ) in degrees. $\newline$ The formula that relates these three variables is $s = r \times \alpha \times (\pi/180)$ , where $\alpha$ is in degrees.
Substitute Values: Substitute the given values into the formula. $\newline$ Given that $\alpha = 60$ degrees and $s = 95$ inches, we can substitute these values into the formula to find the radius $r$ . $\newline$ $95 = r \times 60 \times (\pi/180)$
Simplify Equation: Simplify the equation to solve for $r$ . First, simplify the right side of the equation by multiplying $60$ by $\pi/180$ , which simplifies to $\pi/3$ . $95 = r \times (\pi/3)$ Now, to solve for $r$ , divide both sides of the equation by $\pi/3$ . $r = 95 / (\pi/3)$
Calculate Radius: Calculate the value of $r$ . $r = \frac{95}{(\pi/3)} = 95 \times (\frac{3}{\pi}) \approx 95 \times (\frac{3}{3.14159}) \approx 95 \times 0.95493 \approx 90.71835$ Round the result to the nearest hundredth. $r \approx 90.72$ inches