Question 1149167: a goat is tied outside a triangular fenced garden at point A. the sides of the fence are AB=8m, BC=9m, and CA=12m. if the rope with which the goat is tied is 14m long, find the area over which the goat can graze outside the fence.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! a goat is tied outside a triangular fenced garden at point A. the sides of the fence are AB=8m, BC=9m, and CA=12m. if the rope with which the goat is tied is 14m long, find the area over which the goat can graze outside the fence.
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Find the 3 angles.
Side a (opposite angle A) = 9
Side b = 12
Side c = 8
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c^2 = a^2 + b^2 - 2ab*cos(C)
64 = 81 + 144 - 216cos(C)
cos(C) = 161/216
C =~ 41.809 degs
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sin(C)/c = sin(B)/b
sin(B) = b*sin(C)/c
B =~ 89.6 degs
A = 180 - (B+C) = 48.59 degs
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Calculate the area of the 14 meter radius area.
A = pi*14^2*(360 - 48.59)/360 sq meters
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At point B, the radius is 6 and the central angle is 180 - B degs.
At point C, the radius is 2 and the central angle is 180 - C degs.
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Add the 3 areas.
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