Gret if sum1 could help thansk in advance just a segment (circle) Q

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A goat tethered by a 10-meter rope can graze an area of 269 m², limited by a straight fence 6 meters away from the post. To determine the grazing area, the problem involves calculating the angle formed by the rope and the fence, which creates two right triangles. The angle can be found using the cosine function, specifically cos^{-1}(6/10), and the total angle is double that value. The initial confusion arose from only considering the sector of the circle rather than the entire grazing area. Understanding the full circle is essential for accurate area calculation.
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A goat is tethered to a post by a rope that is ten meters long. The goat is able to graze over any area that the rope allows it to reach other than that excluded by a straight fence. The perpendicular distance from the post to the fence is 6m. Over wat area can the goat graze- to the nearest meter...ans = 269m^2

If any1 could help me determine the required angle ...that would be awesome...since the Q is straigforward after that! thanks
 
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ku1005 said:
A goat is tethered to a post by a rope that is ten meters long. The goat is able to graze over any area that the rope allows it to reach other than that excluded by a straight fence. The perpendicular distance from the post to the fence is 6m. Over wat area can the goat graze- to the nearest meter...ans = 269m^2

If any1 could help me determine the required angle ...that would be awesome...since the Q is straigforward after that! thanks
Draw a picture! You should see two right triangles where the hypotenuse is the 10 m rope and one leg is the 6 m perpendicular distance. The angle those make is one right triangle is obviously
cos^{-1}(\frac{6}{10})
The total angle is twice that.
 
thanks very much...but it was really stupid wat i was actually doin...i wasn;t including the rest of the circle!i only included the sector which i was caclulating with the angle u define above...but since the answer i got was wrong iassumed the angle was wrong...cheers anyway!
 

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