SOLUTION: The three sides of a triangle are 7, 24, and 30 units long. Is the triangle acute, right or obtuse? You must support your answer with computations.

Question 286259: The three sides of a triangle are 7, 24, and 30 units long. Is the triangle acute, right or obtuse? You must support your answer with computations.
Found 2 solutions by stanbon, dabanfield:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The three sides of a triangle are 7, 24, and 30 units long. Is the triangle acute, right or obtuse? You must support your answer with computations.
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Use the Law of Cosines:
cos(A) = (7^2 + 24^2-30^2)/(2*7*24) = -0.81845
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A = cos^-1(-0.81845) = 144.94 degrees
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cos(B) = (30^2+7^2-24^2)/(2*30*7)
cos(B) = 0.8881
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B = cos^-1(0.8881) = 27.37 degrees
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cos(C) = (30^2+24^2-7^2)/(2*30*24) = 0.9910
C = cos^-1(0.9910) = 7.70 degrees
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Cheers,
Stan H.
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
For background see the link below:
http://mathworld.wolfram.com/ObtuseTriangle.html
Let a = 7, b = 24 and c = 30.
a^2 = 49, b^2 = 624 and c^2 = 900
If the triangle is a right triangle then a^2 + b^2 = c^2
Since 7^2 + 24^2 is not equal to 30^2 it's not a right triangle.
Since 7^2 + 24^2 is less than 30^2 the triangle is obtuse
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