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A beam from a lighthouse is visible for a distance of 3 mi.

To the nearest square mile, what is the area covered by the
beam as it sweeps in an arc of 150°?

1 Answer

4 votes

Answer:

The beam from the lighthouse covers a circular area, and we are given that the maximum distance at which the beam is visible is 3 miles. This means that the radius of the circle is 3 miles.

To find the area of the circle covered by the beam as it sweeps in an arc of 150°, we need to calculate what fraction of the circle's total area corresponds to this arc. To do this, we can use the formula:

fraction of circle's area = (central angle of arc / 360°)

In this case, the central angle of the arc is 150°, so the fraction of the circle's area covered by the arc is:

fraction of circle's area = 150° / 360°

fraction of circle's area = 5/12

Therefore, the area covered by the beam is:

area = fraction of circle's area x total area of circle

area = (5/12) x π x radius^2

area = (5/12) x π x 3^2

area = 3.93 square miles (rounded to the nearest square mile)

Therefore, the area covered by the beam as it sweeps in an arc of 150° is approximately 3.93 square miles.

Simple explanation:

The area covered by the beam from the lighthouse as it sweeps in an arc of 150° is approximately 3.93 square miles (rounded to the nearest square mile).

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