SOLUTION: A triangle with a perimeter of 20cm. Two angles are 30 and 50. What are the lengths of the sides in cm.

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Question 255619: A triangle with a perimeter of 20cm. Two angles are 30 and 50. What are the lengths of the sides in cm.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
A triangle with a perimeter of 20cm. Two angles are 30 and 50. What are the lengths of the sides in cm.

Since the sum of the three angles of any triangle is 180°, we
have that the third angle is 180° - (30°+50°) = 180° - 80° = 100° 

I'll arbitrarily let angle A = 30°, angle B = 100°, and angle C = 50°

By the law of sines,

a%2Fsin%28%2230%B0%22%29=b%2Fsin%28%22100%B0%22%29

a%2Asin%28%22100%B0%22%29=b%2Asin%28%2230%B0%22%29

a=%28b%2Asin%28%2230%B0%22%29%29%2Fsin%28%22100%B0%22%29


c%2Fsin%28%2250%B0%22%29=b%2Fsin%28%22100%B0%22%29

c%2Asin%28%22100%B0%22%29=b%2Asin%28%2250%B0%22%29

c=%28b%2Asin%28%2250%B0%22%29%29%2Fsin%28%22100%B0%22%29

Perimeter = a + b + c = 20, so substituting in

a+%2B+b+%2B+c+=+20,









a=%28b%2Asin%28%2230%B0%22%29%29%2Fsin%28%22100%B0%22%29








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c=%28b%2Asin%28%2250%B0%22%29%29%2Fsin%28%22100%B0%22%29

c=%28b%2Asin%28%2250%B0%22%29%29%2Fsin%28%22100%B0%22%29












Edwin