Question 1132346

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 if {{{PSQ = 90}}}°, than {{{RSQ=90}}}°

=>  triangle {{{PSR }}}is similar to triangle {{{RSQ}}}, corresponding sides are proportional

=> side {{{SR= 16cm}}} is common side

=>{{{ SR/PS=SR/SQ}}}

=> {{{16/9=16/SQ}}}

=> {{{16SQ=16*9}}}

=> {{{SQ=16*9/16}}}

=> {{{SQ=9cm}}}

then angle {{{QRS}}} is: 

{{{tan(QRS)=SQ/SR=9/16=0.5625}}}

angle {{{QRS=tan^-1(0.5625)=29.36}}}°