Question

find the cosine of angle E

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

Angle E corresponds with angle I

Answer 1

We have a 5-12-13 right triangle (JI = 5, JH = 12, HI = 13). Angle E corresponds to angle I, so cos(E) = cos(I).

In triangle JHI the hypotenuse is 13 and the side adjacent to angle I is JI = 5, so

cos E = cos I = adjacent/hypotenuse = 5/13.

(If your vertex labeling is different, tell me which vertex is the right angle and I’ll adjust.)