We appreciate your visit to 20 A construction worker during their break decides to draw an arc using a large crane The crane reaches out to a maximum distance of. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To draw an arc that is 60 feet long with a maximum crane reach of 21 feet, the construction worker needs to turn the crane by an angle of approximately 161.62 degrees. The area covered by the sprinkler that can shoot water up to 17 meters and rotate by 42 degrees is approximately 314.16 square meters.
To find the angle needed to draw the arc, we can use the concept of the arc length formula. The formula for finding the length of an arc is given by:
Arc length = r * θ
where r is the radius (maximum distance of the crane reach) and θ is the angle turned by the crane. Rearranging the formula, we can solve for the angle:
θ = Arc length / r
Plugging in the values, we have:
θ = 60 feet / 21 feet = approximately 2.857 radians
To convert radians to degrees, we can use the conversion factor: 180 degrees = π radians. Therefore:
θ = 2.857 * (180 / π) ≈ 161.62 degrees
So, the construction worker needs to turn the crane by an angle of approximately 161.62 degrees to draw the desired arc.
To find the area covered by the sprinkler, we can use the formula for the area of a sector. The formula is given by:
Area = (θ / 360) * π * [tex]r^2[/tex]
where θ is the angle turned by the sprinkler and r is the maximum distance it can shoot water.
Plugging in the values, we have:
Area = (42 / 360) * π * [tex](17 meters)^2[/tex]
Area ≈ 0.116 * 3.1416 * 289 square meters
Area ≈ 314.16 square meters
Therefore, the area covered by the sprinkler is approximately 314.16 square meters.
Learn more about arc length formula
https://brainly.com/question/30650829
#SPJ11
Thanks for taking the time to read 20 A construction worker during their break decides to draw an arc using a large crane The crane reaches out to a maximum distance of. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
