(Q23)In right angle triangle △PQR, right angle is at Q and PQ = 6 cms, ∠RPQ = 60°. Determine the lengths of QR and PR.

Given that △PQR is a right angled triangle, right angle is at Q and PQ = 6 cm, ∠RPQ = 60°.

tan 60° =
side to ∠P
side to ∠P
√ =

which gives RQ = √3 cm ..........(1)

To find the length of the side RQ, we consider

sin 60° =
⇒
√
2
 =
√3
RP
[from (1)]
RP = √3 ×
√3
 = cm

∴ The length of QR is √3 and RP is cm.