Find the radius of the circle if an arc of length 5 ft on the circle subtends a central angle of 135°. (Round your answer to two decimal places.)

5 ft : 135° = x ft : 360°

5/135 = x/360
x = 40/3 ft

This is the whole length of the circle or the circumference. To get the radius,
C = 2πr
r = C / 2π
r = 40/3 / (2*3.14)
r = 2.12 ft

Given a central angle of q = 35° and a radius of 1.5 inches, calculate the arc length of the arc formed from the two radii that make up that central angle.

Well, let's get to the calculations. The length of an arc on a circle can be calculated using the formula:

Arc Length = (Central Angle/360) x 2πr,

where r is the radius of the circle.

In this case, we are given that the arc length is 5 ft and the central angle is 135°. Plugging these values into the formula, we get:

5 = (135/360) x 2πr.

Now, let's do some algebra to solve for r:

5 = (3/8) x 2πr.

Simplifying further:

5 = (3π/4) x r.

Now, let's solve for r by dividing both sides of the equation by (3π/4):

r = (5 x 4) / (3π).

Calculating this out, we get:

r ≈ 6.37 ft.

Therefore, the radius of the circle is approximately 6.37 ft. Now, I'm not saying this circle is clown-sized, but it certainly has a pretty long arc! Keep on clowning around with those math problems!

To find the radius of the circle, you can use the formula:

radius = (arc length) / (central angle in radians)

In this case, the arc length is given as 5 ft and the central angle is given as 135°:
1. Convert the central angle from degrees to radians:
central angle in radians = (central angle in degrees) * (π / 180)
central angle in radians = 135° * (π / 180) = (135 * π) / 180 radians

2. Plug the values into the formula to find the radius:
radius = (arc length) / (central angle in radians)
radius = 5 ft / [(135π) / 180] radians

3. Simplify the expression and round the answer to two decimal places:
radius ≈ 2.87 ft

Therefore, the radius of the circle is approximately 2.87 feet.

find the arc of 150 an 18