Question 1111462: A gardener needs to cultivate a triangular plot of land. One angle of the garden is 47,and two sides adjacent to the angle are 77 feet and 76 feet. What is the area of the plot of land.
Found 4 solutions by Boreal, rothauserc, TeachMath, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! find third side by using Law of Cosines
c^2=a^2+b^2-2abcos C=77^2+76^2-2(76)(77)cos 47
=11705-11704 * 0.682
=11705-7982.13
=3722.87
c=61.01, use 61
Heron's formula
A= sqrt (s*(s-a)(s-b)(s-c)), s= (1/2)(a+b+c)=107
A=sqrt (107*40*41*46)=2841 ft^2
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! Use the law of cosines to get the length(l) of the third side
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l^2 = 77^2 + 76^2 - 2 * 77 * 76 * cos(47)
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l^2 = 3722.8912
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l = 61.0155
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use Heron's formula to calculate the area of the triangle
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s = (77 + 76 + 61.0155)/2 = 107.0078
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Area of triangle = square root(s * (s-a) * (s-b) * (s-c))
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Area of triangle = square root(107.0078 * (107.0078-77) * (107.0078-76) * (107.0078-61.0155)) = 2,139.9461 square feet
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Note that this solution works in all cases, the solution given by tutors that does not include the law of cosines fails when the included angle is > 90 degrees
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Answer by TeachMath(96)  (Show Source):
You can put this solution on YOUR website! Since the ANGLE is INCLUDED or it's between the 2 sides, then the AREA is SIMPLY: 1/2 * 77 * 76 * Sin 47 = 2,139.940931 sq ft.
This is ALL that it takes.
Answer by ikleyn(52795)  (Show Source):
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