Question 630756: The angles of a triangle are 30, 70 & 80 degrees.
The perimeter is 12 units.
What are the sides?
Answer by dfrazzetto(283)   (Show Source):
You can put this solution on YOUR website! A = 30 degrees
B = 70 degrees
C = 80 degrees
sides are a, b, c
P = a + b + c = 12
This is an AAA triangle, we know all angles but no sides; we cannot solve explicitly for the sides, but we can find their ratios, and use the perimeter to find the lengths.
Sine Rule:
a/sinA = b/sinB = c/sinC
a/(sin30) = b/(sin70) = c/(sin80)
a/(.5) = b/(.93969) = c/(.9848)
Assuming a = 1, b = 1.8794, c = 1.9696
Compare the perimeter of this similar triangle to a perimeter of 12 units, and you'll get a scaling factor:
p = 1 + 1.8794 + 1.9696 = 4.849 units
scaling factor = P/p = 12 units / 4.849 units = 2.47473706
Multiple the similar "base" triangle by this scaling factor, you get
a = 1*2.47473706; b = 1.8794*2.47473706; c = 1.9696*2.47473706
approximately, you get:
a = 2.475; b = 4.651; c = 4.874
a + b + c = 12
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