Question 73

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 :

Solution

$$\angle PTS + \angle STR = 180\degree$$

$$\angle PTS = 180 - 122 = 58\degree$$

$$\angle$$ P is a common angle.

$$\triangle$$ PQR and $$\triangle$$ PTS are similar triangle. SO,

$$\frac{PT}{PQ} = \frac{PS}{PR}$$

$$\frac{12}{24} = \frac{14}{PR}$$

PR = 28 cm

RT = PR - PT = 28 - 12 = 16 cm

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