Solution.
a=5in;a=5 in;a=5in;
b=12in;b=12in;b=12in;
c=13in;c=13in;c=13in;
By the cosine theorem we find the angle against the larger side:
с2=a2+b2−2abcosγ; ⟹ cosγ=a2+b2−c22ab;с^2=a^2+b^2-2abcos\gamma;\implies cos\gamma=\dfrac{a^2+b^2-c^2}{2ab};с2=a2+b2−2abcosγ;⟹cosγ=2aba2+b2−c2;
cosγ=25+144−1692⋅5⋅12=0;cos\gamma=\dfrac{25+144-169}{2\sdot5\sdot12}=0;cosγ=2⋅5⋅1225+144−169=0;
γ=90o;\gamma=90^o;γ=90o;
Answer: The sides form a right angle.
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