Final answer:
To calculate the intercepted arc length ABD for an angle of 20 degrees in a circle with a radius of 4 feet, use the formula arc length = (θ/360) × 2πr. The calculation gives approximately 4.4 feet, so the length rounded to the nearest tenth is 4.7 feet which is option (a).
Step-by-step explanation:
The student has asked to determine the length of the intercepted arc ABD in a circle with a radius of 4 feet where ∠AOB measures 20 degrees. To find the arc length ABD, we can use the formula arc length = (θ/360) × 2πr, where θ is the central angle in degrees, r is the radius of the circle, and π is Pi, approximately 3.14. In this case, θ is 20 degrees and r is 4 feet.
Plugging the values into the formula, we get arc length ABD = (20/360) × 2 × 3.14 × 4 ≈ (1/18) × 3.14 × 8 ≈ 0.555... × 8 ≈ 4.4 feet. Since the options provided are rounded to the tenths place, the closest answer is 4.7 feet, which corresponds to option (a).
To determine the length of the intercepted angle ABD, we need to find the length of the arc AB on the circle. The formula to find the length of an arc in a circle is given by:
Length of the arc = (angle in degrees / 360 degrees) * (circumference of the circle)
In this case, the angle AO is given as 20 degrees, and the circumference of the circle is 2*pi*r, where r is the radius. Substituting the values, we have:
Length of the arc AB = (20 / 360) * (2 * 3.14 * 4) = 1.76 feet (rounded to the nearest tenth)