Answer to Question #117625 in Geometry for Erika Reed

Question

State if the three side lengths form an acute, obtuse, or right triangle. ( 5 in, 12 in, 13 in ) *

Answer 1

Solution.

$a=5 in;$

$b=12in;$

$c=13in;$

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

$с^2=a^2+b^2-2abcos\gamma;\implies cos\gamma=\dfrac{a^2+b^2-c^2}{2ab};$

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

$\gamma=90^o;$

Answer: The sides form a right angle.