Question

Suppose that Juan found a crop circle with a 1350 ft radius. He follows a 2000 ft arc on the circle.What central angle, in radians, would intercept this arc?

Answer 1

Given:

a.) Suppose that Juan found a crop circle with a 1350 ft radius.

b.) He follows a 2000 ft arc on the circle.

To find the central angle, we will be using the following formula:

`\text{ S = r}\Theta`

Where,

S = Arc Length = 2000 ft.

r = radius = 1350 ft.

Θ = Central angle (in radians)

We get,

`\text{ S = r}\Theta`
`\Theta\text{ = }\frac{\text{ S}}{\text{ r}}\text{ = }\frac{\text{ 2000}}{\text{ 1350}}\text{ = }\frac{\text{ 40}}{\text{ 27}}`
`\text{ }\Theta\text{ = }(40)/(27)\text{ radians}`

Therefore, the answer is 40/27 radians.