Question

In ΔPQR, PS is perpendicular to QR. If PS = 6 cm, find the length of QR.

Answer 1

Given:

In △PQR

PS ⊥ QR

PS = 6 cm

∠PQR = 60°

∠PRQ = 30°

Length of QR

Step 1: In triangle △PQS

∠Q = 60° 

PS = 6

`tan(60°) = (PS)/(QS)`

= `sqrt3 = 6/(QS)`

= QS = `6/sqrt3`

= `2 sqrt3`

Step 2:

In triangle △PRS:

∠R = 30°

PS = 6

tan(30°) = `(PS)/(RS)`

= `1/sqrt3 = 6/(RS)`

= RS = `6sqrt3`

Step 3: 

= QR = QS + RS 

= `2sqrt3 + 6sqrt3`

= `8sqrt3` cm