In $\triangle PQR, PQ = 24$ cm and $\angle Q = 58^\circ$ S and T are the points on side PQ and PR, respectively, such that $\angle STR = 122^\circ$ and If PS = 14 cm and PT = 12 cm, then the length of RT is :

16 cm

PR is a straight line

∠PTS + 122º = 180º

∠PTS = 58º

In triangle PQR and PST

∠P is common

∠PTS = ∠PQR  

Triangle PQR ∼ PTS

\(\frac{PR}{PS}\) = \(\frac{PQ}{PT}\)

\(\frac{PR}{14}\) = \(\frac{24}{12}\)

\(\frac{PR}{14}\) = \(\frac{24}{12}\)

PR = 28 cm

We know,

PR = PT + RT

28 = 12 + RT

RT = 16 cm