Question

in LMN, S is the centroid. If SQ=22 find LS

Answer 1

In this problem we know that SQ is equal to 22, we also know that the angle Q is equal to 90º and all the angles in the middle are the same and will be:

$\frac{360}{6}=60$

So if we separete each triangle we can find the missing angle that will be equal to 30º like this:

So now we can use the sin law to find the side SN that will be equal to the side LS so:

$\begin{gathered} \frac{22}{\sin(30)}=\frac{SN}{\sin (90)} \\ SN=\frac{22}{\frac{1}{2}} \\ SN=44 \end{gathered}$

So the lenght of LS is 44