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 :
Answer & explanation
Correct answer: option 2
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