Question

find the tangent of angle S

there are two similar right triangles, one has unknown lengths and angles which are classified as S, U, T, the other triangle has Line XW which has a length of 17, Line WV which has a length of 15, and Line XV which has a length of 8

Angle S corresponds with angle W

Answer 1

First note 8^2 + 15^2 = 64 + 225 = 289 = 17^2, so XW = 17 is the hypotenuse and the right angle is at V.

For angle W the opposite side is XV = 8 and the adjacent side is WV = 15, so
tan W = 8/15.

Since angle S corresponds to W, tan S = 8/15 (≈ 0.5333).