find the arc length of AB to the nearest tenth. AB equals 45 degrees. radius is 5 in.
The radius of the whole circle = 2πr
= 10π
Now, what fraction of that circumference is a 45 degree sector?
To find the arc length of AB, you can use the formula:
Arc Length = (angle/360) * circumference
Given:
Angle (AB) = 45 degrees
Radius (r) = 5 inches
First, let's calculate the circumference:
Circumference = 2 * π * r
Substituting the given values:
Circumference = 2 * π * 5 inches
Circumference ≈ 31.4 inches (rounded to the nearest tenth)
Now, let's calculate the arc length:
Arc Length = (45/360) * 31.4 inches
Arc Length ≈ 3.93 inches (rounded to the nearest tenth)
Therefore, the arc length of AB is approximately 3.93 inches.
To find the arc length of a circle, you can use the formula:
Arc Length = (θ/360) × 2πr
Where:
- θ represents the angle in degrees
- r represents the radius of the circle
In this case, AB is given as 45 degrees and the radius is 5 inches. Plugging in these values into the formula, we have:
Arc Length = (45/360) × 2π × 5
Simplifying further:
Arc Length = (1/8) × 2 × π × 5
Arc Length = (1/8) × 10π
Arc Length = (10π)/8
Arc Length = 5π/4
To find the arc length to the nearest tenth, we can approximate π as 3.14:
Arc Length ≈ (5 × 3.14)/4
Arc Length ≈ 15.7/4
Arc Length ≈ 3.925
Therefore, the arc length of AB, rounded to the nearest tenth, is approximately 3.9 inches.