Given that RS = 6, ST = 3, and SL = 4, to find NS, we first find QS.
Notice that NQS forms a right triangle with the right andle at Q.
To find QS, we notice that QRS forms a right triangle with the right angle at R.
Note that ST = QR = 3 and RS = 6.
Using pythagoras theorem
[tex]QS^2=QR^2+RS^2=3^2+6^2=9+36=45 \\ \\ QS=\sqrt{45}[/tex]
Note that NQ = SL = 4.
Using pythagoras theorem
[tex]NS^2=NQ^2+QS^2=4^2 + 45=61 \\ \\ NS= \sqrt{61} [/tex]
