Question

find the tangent of angle Z

there are two similar right triangles, one has unknown lengths and angles which are classified as Y, X, Z, the other triangle has Line VU which has a length of 24, Line VW which has a length of 10, and Line WU which has a length of 26

Angle Z corresponds with angle U

Answer 1

tan(Z) = tan(U). In triangle VWU, WU = 26 is the hypotenuse (10^2 + 24^2 = 26^2), so the right angle is at V. For angle U the opposite side is VW = 10 and the adjacent leg is VU = 24. Thus

tan(Z) = tan(U) = 10/24 = 5/12.