A wheel with a 20-inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 3 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks?
someone helped me on this before: angle/360=3/(40pi), i know i have to solve for angle..but i still don't get the answer..
A. 4.6 degrees
B. 10.6 degrees
C. 6.6 degrees
D. 8.6 degrees
for small angles, angle in radians is about the arc length over radius
3/20 = .15 radians
.15 * 360/2 pi = 8.6 deg
THANKSSS<33
To find the angle between the radii to the two marks, we can use the formula:
angle / 360 = arc length / circumference
In this case, the arc length is 3 inches and the circumference can be calculated using the formula 2πr, where r is the radius. Substituting the given radius of 20 inches into the formula, we get:
Circumference = 2π(20) = 40π inches
Now let's substitute the values into the formula for the angle:
angle / 360 = 3 / (40π)
To solve for the angle, we can cross-multiply:
angle = (3 * 360) / (40π)
angle = 1080 / (40π)
angle ≈ 8.59 degrees
Rounding to the nearest tenth of a degree, the angle between the radii to the two marks is approximately 8.6 degrees. Therefore, the correct answer is D. 8.6 degrees.
To solve for the angle between the radii to the two marks, we can use the formula given: angle/360 = 3/(40π).
To find the angle, we need to isolate it on one side of the equation. Let's start by cross-multiplying:
angle = (3 * 360) / (40π)
Now, let's simplify further by calculating the numerator:
angle ≈ 1080 / (40π)
To get the answer to the nearest tenth of a degree, we need to evaluate this expression using a calculator or computer. Let's use this formula:
angle ≈ 1080 / (40 * 3.14159)
Calculating this using a calculator, we get:
angle ≈ 8.6 degrees
Therefore, the angle between the radii to the two marks is approximately 8.6 degrees. So, the correct answer is option D. 8.6 degrees.