Q. 54.4( 22 Votes )

In right angle tr

Answer :


To find QR:


Since, tan θ = perpendicular/base


We know that,



[, PQ = 6 cm & tan 60° = √3]


QR = 6√3


Now, PR can be found by two ways -


1st method: In ∆PQR, using Pythagoras theorem,


PR2 = PQ2 + QR2 [, (hypotenuse)2 = (perpendicular)2 + (base)2]


PR2 = 62 + (6√3)2


PR2 = 36 + 108 = 144


PR = √144 = 12


2nd Method:


Since, cos θ = base/hypotenuse


We know that,





PR = 2 × PQ


PR = 2 × 6 = 12


Thus, QR = 6√3 cm and PR = 12 cm.


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