Wp tag in header not bringing up subtemplate css

<!--   engineer subtemplate  -->
	<?php if(is_page_template('engineeringST.php')) {?>
	<link rel="stylesheet" href="<?php bloginfo('template_url'); ?> /css/engST.css">
		<?php }?>
		
	<!--   engineer subtemplate  -->
	<?php if(is_page_template('engineeringST.php')) {?>
	<link rel="stylesheet" href="<?php bloginfo('template_url'); ?> ./css/engST.css">
	<?php }?>
	
	<!--   engineer subtemplate  -->
	<?php if(is_page_template('engineeringST.php')) {?>
	<link rel="stylesheet" href="<?php bloginfo('template_url'); ?> ../css/engST.css">
	<?php }?>

tried a variation of each tag above.
not one of them is bringing in the css for this subtemplate. What am I doing wrong???
And yes, i have a page titled engineeringST.php with the tags at top identifying it as a template.

<?php /*
Template Name: egnineeringST
*/
?> 

& in the wp-admin pages section i went to the engineering page, and in the “page attribute” section from the template drop down menu I picked engineeringST.

Thx
D