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

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In summary, the goat can graze over an area of 269m^2, and the required angle for the rope is twice the inverse cosine of 6/10.
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ku1005
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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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  • #2
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
[tex]cos^{-1}(\frac{6}{10})[/tex]
The total angle is twice that.
 
  • #3
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!
 

What is a segment (circle) Q?

A segment (circle) Q is a mathematical term that refers to a part of a circle, specifically the portion of the circle enclosed by an arc and its corresponding chord.

How do you find the area of a segment (circle) Q?

The area of a segment (circle) Q can be found by first calculating the area of the corresponding sector (the portion of the circle enclosed by the arc and two radii) and then subtracting the area of the triangle formed by the radii and the chord. The formula for the area of a segment (circle) Q is A = (r²/2)(θ-sinθ), where r is the radius of the circle and θ is the central angle of the segment (in radians).

What is the central angle of a segment (circle) Q?

The central angle of a segment (circle) Q is the angle formed by the two radii of the circle that connect to the endpoints of the arc that forms the segment. It is measured in radians and is equal to the ratio of the arc length to the radius of the circle.

How do you find the length of an arc in a segment (circle) Q?

The length of an arc in a segment (circle) Q can be found by first finding the central angle of the segment (in radians) and then using the formula s = rθ, where s is the arc length and r is the radius of the circle. Alternatively, you can use the formula s = 2πr(n/360), where n is the degree measure of the central angle.

What is the relationship between a segment (circle) Q and a sector?

A segment (circle) Q and a sector are both parts of a circle, with the sector being the larger portion enclosed by the arc and two radii, and the segment being the smaller portion enclosed by the arc and its corresponding chord. The area and central angle of a segment (circle) Q are always less than or equal to the area and central angle of the corresponding sector.

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