Question

Given RS=6, ST=3, and SL=4, find the required measure. (Part of the answer is provided for you)

NS=

Answer 1

`\sqrt 61`Answer:

Explanation:

Answer 2

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

`QS^2=QR^2+RS^2=3^2+6^2=9+36=45 \\ \\ QS=√(45)`

Note that NQ = SL = 4.

Using pythagoras theorem

`NS^2=NQ^2+QS^2=4^2 + 45=61 \\ \\ NS= √(61)`