Question

The beam of a lighthouse is visible for a distance of 15 mi. To the nearest square mile, what is the area covered by the beam as it sweeps in an arc of 270°?

Answer 1

Explanation:

Alright, lets get started.

The light house light is making an arc, so please refer the diagram I have attached.

The angle is 270 degree. Converting it into radians :

`270*(\pi )/(180)  = 4.7124`

The radius of the arc will be = 15 m

So, area of the arc will be =
`(1)/(2)*angle*radius^2`

So, area of the arc will be =
`(1)/(2)*4.7124*15^2`

So, area of the arc
`= 530.143`

To the nearest square meter, the area id 530 square meters. : Answer

Hope it will help :)

Answer 2

area of circle = pi x r^2

using 3.14 for pi

area = 3.14 x 15^2 = 706.5 square miles

270/360 = 0.75

706.5 * 0.75 = 529.875

rounded to nearest mile = 530 miles