Question #117625
State if the three side lengths form an acute, obtuse, or right triangle. ( 5 in, 12 in, 13 in ) *
1
Expert's answer
2020-05-22T15:03:02-0400

Solution.

a=5in;a=5 in;

b=12in;b=12in;

c=13in;c=13in;

By the cosine theorem we find the angle against the larger side:


с2=a2+b22abcosγ;    cosγ=a2+b2c22ab;с^2=a^2+b^2-2abcos\gamma;\implies cos\gamma=\dfrac{a^2+b^2-c^2}{2ab};

cosγ=25+1441692512=0;cos\gamma=\dfrac{25+144-169}{2\sdot5\sdot12}=0;

γ=90o;\gamma=90^o;

Answer: The sides form a right angle.


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