Question

find the Tangent of angle F

there are two similar right triangles, one has unknown lengths and angles which are classified as G, H, F, the other triangle has Line JK which has a length of 5, Line JI which has a length of 12, and Line KI which has a length of 13

Angle F corresponds with Angle I

Answer 1

Because the triangles are similar, tan(F) = tan(I). In triangle JKI the hypotenuse KI = 13, so the right angle is at J. For angle I the opposite side is JK = 5 and the adjacent side is JI = 12. Thus

tan F = tan I = 5/12 ≈ 0.4167.