Given △ABC ~ △XYZ, what is the value of cos(Z)? I need help understanding why this is the answer I need an explanation. Thank you
Accepted Solution
A:
It is 12/13.
Since the triangles are similar, the corresponding angles are congruent. This means that m∠C = m∠Z, and that cos C = cos Z.
The ratio for cosine is adjacent/hypotenuse;
cos C = 12/13, since the side marked 12 is adjacent to angle C and 13 is the hypotenuse of this triangle. Since the angles and cosines for C and Z will be the same, cos Z = 12/13 as well.