SOLUTION: Given that the perimeter of a triangle is 180 in. If the angles of the triangle are in the ration 5:6:7. Determine the sides of the triangle.

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Question 1112168: Given that the perimeter of a triangle is 180 in. If the angles of the triangle are in the ration 5:6:7. Determine the sides of the triangle.
Answer by Alan3354(69443) About Me  (Show Source):
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Given that the perimeter of a triangle is 180 in. If the angles of the triangle are in the ration 5:6:7. Determine the sides of the triangle.
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The angles are 50, 60 & 70 degs
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A = 50
B = 60
C = 70
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Pick a number for one of the sides.
eg, side a = 5
Find sides b & c:
a/sin(A) = b/sin(B) = c/sin(C)
5/sin(50) = b/sin(60)
b = (5*sqrt(3)/2)/sin(50)
b =~ 5.6526
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5/sin(50) = c/sin(70)
c = 5*sin(70)/sin(50)
c =~ 6.1334
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a + b + c =~ 16.786
Adjust to make the sum 18
a = 5*(18/16.786) = 5.3616
b = 5.6526*(18/16.786) = 6.0614
c = 6.1334*(18/16.786) = 6.577
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