SOLUTION: The sides of a triangular field have lengths 80m, 90m and 100m. Calculate the area of the field to the nearest metres squared. YOu use the cos rule for this I think?

Algebra ->  Trigonometry-basics -> SOLUTION: The sides of a triangular field have lengths 80m, 90m and 100m. Calculate the area of the field to the nearest metres squared. YOu use the cos rule for this I think?      Log On


   

Question 1111114: The sides of a triangular field have lengths 80m, 90m and 100m. Calculate the area of the field to the nearest metres squared.
YOu use the cos rule for this I think?
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
You use Heron's formula:
Area = sqrt(p(p-a)(p-b)(p-c)) where p is half the perimeter and a = 80, b = 90,and c = 100. So let's do it:
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(80+90+100)/2 = 135
Let's plug in all the numbers into the formula:
Area = sqrt(135(135-80)(135-90)(135-100))
= sqrt(135(55)(45)(35))
Now, because of the distributive properties of multiplication, we can either multiply 135 times each number in parenthesis and then multiply those numbers among themselves, or you can multiply the numbers in parenthesis and then multiply the result times 135, or just multiply across. This is what I am going to do:
sqrt(135 x 55 x 45 x 35)
sqrt(11694375) = 3,419.70 m^2
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Happy learning,
John