Concept explainers
To find: The maximum grazing area of the cow.
Answer to Problem 46AYU
The total area that the cow grazes is
Explanation of Solution
Given:
The given diagram is shown in Figure
Figure
The length of the rope is
Calculation:
Consider the cow grazes
Then,
Consider the barn is 10 ft by 10 ft square so at the corners the rope will remain 10 ft shorter or 90 ft only. As the cow comes from both the sides the arc of the paths overlap at point U as shown in Figure. The joining of the intersecting point to the corners of the barn forms the triangle PUR.
Consider the right angle triangle PQR by Pythagoras theorem is,
Consider the semi perimeter of the triangle is,
The area of the triangle by Heron’s formula is,
Consider the area of the gazing part inside is its difference of the area of the half barn inside the triangle that is,
To determine the angle
`
Consider by angle sum property,
To determine the angle
`
Consider by angle sum property,
Then, the area of the sector TPS is,
Then, the area of the sector SRU is,
Then, the total area that the cow grazes is,
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