Question

find the Tangent of angle D

there are two similar right triangles, one has unknown lengths and angles which are classified as F, H, D, the other triangle has Line FG which has a length of 24, Line FE which has a length of 70, and Line GE which has a length of 74

Angle D corresponds with angle E

Answer 1

First note FG^2 + FE^2 = 24^2 + 70^2 = 576 + 4900 = 5476 = 74^2, so GE = 74 is the hypotenuse and the right angle is at F.

For angle E the opposite side is FG = 24 and the adjacent side is FE = 70, so
tan E = 24/70 = 12/35.

Since D corresponds to E in the similar triangles, tan D = tan E = 12/35 ≈ 0.342857.