Question

If triangles are similar, state how (AA, SAS, or SSS)

Answer 1

Ok, let's find the side HT to help us decide:

$32^2=30^2+HT^2$

Clearing HT:

$32^2-30^2=HT^2$$1024-900=HT^2$$124=HT^2$$HT=\sqrt[]{124}$

And, now let's find SW:

$\begin{gathered} SW^2=48^2-44^2=2304-1936=368 \\ SW=\sqrt[]{368} \end{gathered}$

And finally let's calculate the angles:

We know that angles T and Q are equal to 90°

M=arccos(30/32)=arccos(0.9375)=20.36

Q=arc cos(44/48)=arccos=23.55

So, finally we have that ΔMTH ~ ΔQWS is similar by SAS.