Question

Triangles A B C and X Y Z are shown. Angles A B C and X Y Z are right angles. Angles B A C and Y X Z are congruent. The length of A B is 5, the length of A C is 13, and the length of B C is 12.
Given △ABC ~ △XYZ, what is the value of cos(Z)?

Five-thirteenths
Five-twelfths
Twelve-thirteenths
Twelve-fifths

Answer 1

Triangles are similar with C ↔ Z, so cos(Z) = cos(C). In △ABC (a 5-12-13 right triangle) the side adjacent to angle C is 12 and the hypotenuse is 13, so cos(Z) = 12/13.

Answer: Twelve-thirteenths.