Question 1193620

Given:	right △RST with 
RT = 8radical 2
 and m∠
STV = 150°
Find:	RS and ST

△R S T has vertices R on the left, S on top, and T on the right. ∠S is a right angle. A point labeled V lies to the right of T. The horizontal line segment that connects R and T continues to the right and ends at V.
simplest radical form	RS	=	
 
approximation	RS   =	
simplest radical form	ST	=	
 
approximation	ST	=	
<pre>Based on the description, right △RST has its right angle at S. Also, &#8737STR = 30<sup>o</sup> since it's supplementary to straight &#8737RTV. 
We therefore have a 30-60-90 special △ with RT as its hypotenuse.
As △RST is a 30-60-90 special △ with hypotenuse RT being 8√2, RS, the {{{matrix(1,11, Shorter, leg, "=", 8sqrt(2)/2, "=", 4sqrt(2), "(Radical", "form)", or, 5.6568542, "(approximation)")}}}

As △RST is a 30-60-90 special △ with hypotenuse RT being 8√2, ST, the {{{matrix(1,11, Longer, leg, "=", 8sqrt(2) * (sqrt(3)/2), "=", 4sqrt(6), "(Radical", "form)", or, 9.797958971, "(approximation)")}}}

That's IT!! Nothing MORE, nothing LESS!</pre>