Answer:
Option B is correct i.e, [tex]23^{\circ}[/tex]
Explanation:
Law of cosine is useful to find:
* The third side of a triangle when we know two sides and angle between them.
* The angles of a triangle when we know all three sides.
It can be either of these forms;
[tex]\cos C = \frac{a^2+b^2-c^2}{2ab}[/tex]
[tex]\cos A = \frac{b^2+c^2-a^2}{2bc}[/tex]
[tex]\cos B = \frac{c^2+a^2-b^2}{2ca}[/tex]
Given triangle ABC is right angle triangle.
Law of cosines for this triangle is,
[tex]b^2+c^2-2bc\cos A = a^2[/tex]
since,[tex]\angle A = 23^{\circ}[/tex] , [tex]\angle B = 90^{\circ}[/tex] and [tex]\angle C= 67^{\circ}[/tex].
then,
[tex]12^2+13^2-2(12)(13)\cos 23^{\circ} = 5^2[/tex]
