Question 1030006
When we know the three sides of a triangle, we call it an SSS triangle (we know the Side-Side-Side).
To find the angles of an SSS triangle we apply the Law of Cosines to find two of the angles, and the third simply by addition and subtraction, like this:
Let the angles be A, B, and C and the sides a, b, c. And:
a = 300
b = 250
c = 420
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cos C = (a^2+b^2-c^2)/2ab
cos A = (b^2+c^2-a^2)/2bc
cos B = (c^2+a^2-b^2)/2ca
NOTE: They are the same formula, the sides move around depending on which angle you are trying to find
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Finding angle C:
Cos C = (300^2+250^2-420^2)/2(300*250)
Cos C = (90,000+62,500-176,400)/150,000
Cos C = -23,900/150,000
Cos C = -0.159
C = cos^-1(0.159) Use the Cos^-1 function in your calculator
C = 80.85 degrees
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Find angle A:
Cos A = (250^2+420^2-300^2+)/2(300*250)/2(250*420)
Cos A = (62,500+176,400-90,000)/210,000
Cos A = -0.71
A = cos^-1(0.71)= 44.765 degrees
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Find angle B:
B = 180-(80.85+44.765)= 54.385