SOLUTION: a triangle has three angles 110, 50 and 20. the longest side is 5 cm longer than the smallest side. Determine the perimeter of the triangle

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Question 1037280: a triangle has three angles 110, 50 and 20. the longest side is 5 cm longer than the smallest side. Determine the perimeter of the triangle
Answer by Alan3354(69443) About Me  (Show Source):
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a triangle has three angles 110, 50 and 20. the longest side is 5 cm longer than the smallest side. Determine the perimeter of the triangle
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The smallest side is opposite the smallest angle.
x = length of smallest side
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x/sin(20) = (x+5)/sin(110)
x*sin(110) = (x+5)*sin(20) = x*sin(20) + 5sin(20)
x*(sin(110) - sin(20)) = 5sin(20)
x = 5sin(20)/(sin(110) - sin(20))
x =~ 2.861267
Longest side = 7.861267
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Find the 3rd side. Call it s:
x/sin(20) = s/sin(50)
s = x*sin(50)/sin(20)
s =~ 6.40856
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Add those to find the perimeter.