You can count, but there probably is a better solution.

I will not yet give the solution for this problem, but I will enumerate all the triangles that can be identified in the figure instead.

$\Delta ABC$

$\Delta ABD$

$\Delta ABE$

$\Delta ABP$

$\Delta ABQ$

$\Delta ABT$

$\Delta ACD$

$\Delta ACE$

$\Delta ACS$

$\Delta ADE$

$\Delta ADQ$

$\Delta AEP$

$\Delta AES$

$\Delta AET$

$\Delta APT$

$\Delta BCD$

$\Delta BCE$

$\Delta BCP$

$\Delta BCQ$

$\Delta BCR$

$\Delta BDE$

$\Delta BDT$

$\Delta BER$

$\Delta BPQ$

$\Delta CDE$

$\Delta CDQ$

$\Delta CDR$

$\Delta CDS$

$\Delta CEP$

$\Delta CQR$

$\Delta DER$

$\Delta DES$

$\Delta DET$

$\Delta DRS$

$\Delta EST$

The solution is up to you guys! :)