Question

find the cosine of angle Y

there are two similar right triangles, one has unknown lengths and angles which are classified as W, U, Y, the other triangle has Line WV which has a length of 65, Line VX which has a length of 97 and Line WX which has a length of 72

Angle Y corresponds with angle X

Answer 1

Since 65^2 + 72^2 = 4225 + 5184 = 9409 = 97^2, the triangle is right with hypotenuse VX = 97. Angle X is adjacent to side WX = 72, so

cos X = adjacent / hypotenuse = 72/97.

Angle Y corresponds to X, so cos Y = 72/97 ≈ 0.7423.