In ΔPQR, ∠Q = 85° and ∠R = 65°. Points S and T are on the sides PQ and PR, respectively such that ∠STR = 95°, and the ratio of the QR and ST is 9 : 5. If PQ = 21.6 cm, then the length of PT is:

12 cm

In triangle PQR and PST

∠PQR = ∠PTS

∠P is common in both the triangle

⇒ ∠PRQ = ∠PST

Hence triangle PQR ∼ PST

Now,

\(\frac{QR}{ST}\) = \(\frac{PQ}{PT}\)

\(\frac{9}{5}\) = \(\frac{21.6}{PT}\)

PT = \(\frac{21.6 × 5}{9}\)

= 12 cm