AS shown in the figure :
There are two right triangles
For the triangle SYE :
m∠ Y = 90
m∠ E = 39
So, m∠S = 180 - ( 90 + 39 ) = 51
For the triangle WCH :
m∠ C = 90
m∠ W = 51
m∠ H = 180 - ( 90 + 51 ) = 39
So, the triangles SYE and WCH have the following :
m∠ Y = m∠ C = 90
m∠ E = m∠ H = 39
m∠ S = m∠ W = 51
So, the triangles are similar by AAA [ angle - angle - angle Postulate ]