SOLUTION: If the area of traingle is 80 sq unit.the longest side is 20 unit and other side is 10 unit then the third side is what??

Question 1073094: If the area of traingle is 80 sq unit.the longest side is 20 unit and other side is 10 unit then the third side is what??
Answer by ikleyn(52877) (Show Source): You can put this solution on YOUR website!
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If the area of traingle is 80 sq unit.the longest side is 20 unit and other side is 10 unit then the third side is what??
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The area of a triangle (of any triangle) is half the product of two sides lengths and the sine of the angle between them:

S = .


Substituting the given data, you obtain  =  =  =  = .


Then  = +/-  = +/- .


 can not be negative under the given condition.

Indeed, otherwise the angle  is obtuse and our 20 unit side is not the longest side.

So,  = .

Now apply the Cosine Law theorem. You will get for the length of the third side

 =  =  =  =  = 260.

Thus  c =  = 16.125 units (approximately).

Solved.

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